Few things can be as nerve wracking as the usually dependable trail animal that won't cross an obstacle. Mules are often noted for being extremely suspicious of bridges in particular.
The equines I have trained are confident with bridges and will typically doodle right on across with little concern. Many folks ask how I get them that confident. I actually start the process with a tarp. Once you've completed the following exercises and have your animal's confidence with the tarp, you can try crossing a bridge. If you don't have a bridge to work with just use any old piece of plywood lying on the ground. (Make sure there are no nails sticking out of it.)
Here's how I do it.
It all starts with the basic foundation training. From the very first day they arrive, they are handled in a friendly, relaxed, and attentive manner. It's all about the relationship. Now, I don't mean we sit around and eat snacks together all day. On the contrary, we work hard -- at playing. Yes, I said playing. Everyone learns better when they are relaxed, and horses and mules are no exception. We go into the round pen and spend a few minutes getting to know one another. I ask them to move parts of their body, and give instant feedback in the form of release-of-pressure at the exact moment there is even a hint of attempted compliance. Now, this is a simple concept that is difficult to fully explain in print.
The short version is: Motivate with pressure, teach with release, reward with rest.
Let's say I want my mule Benjamin to back away from me. I may start out by simply putting mild pressure on him in the form of stepping forward into his personal space. If he's not paying attention, or even if he is but doesn't catch on to the fact that I'm trying to communicate something to him, he'll most likely stand there blinking at me. He may raise his head curiously, nervously, or even with a hint of annoyance. None of those reactions are "wrong", because he's just telling me how he feels. Try not to assume every response that is different than what you were wanting is defiance. Most often it's actually not, it's just your animal telling you "I have no idea what you are doing or why, but it makes me feel _____." The blank can be anything from scared to bored, amused to apathetic.
The key in all your interaction is to develop a common language and mutual awareness.
So I step further into Benjamin's space and maybe this time hold my hands up as I do so. He reacts by jerking his head up and leaning backwards, and maybe one foot moves back ever so slightly. What do I do? Instead of running at him and being overly aggressive like some folks tend to do, I immediately stop all pressure at the first indications of backward shift and movement. Benjamin's response? Likely he will look surprised, give me a curious look and start to lick his lips, telling me he's mentally digesting what just happened. So to ask him again, I do NOT immediately raise my hands to him, but instead go back to the most subtle cue - one step towards him as I direct a stern look and strong, confident posture (Shoulders squared, standing upright and solid, moving straight towards him) in his direction.
If he doesn't move, I will again increase the pressure I'm puttin on him in incremental stages until he responds with a backwards step. If he were to move any amount backward at the first level of pressure, I would instantly stop and soften my posture and body language, saying "good boy" in a happy and friendly tone.
By instantly stopping and changing my physical as well as vocal tone, I'm telling him he did what I was asking. Chances are there would be some serious lip licking and softening of his posture as he now recognizes that the silly human in front of him actually understands the concept of intelligent communication. Now he'll be looking and waiting for other chances to see what this odd hairless creature might try to say next.
Now that I've got him moving away, I will soften my body language even more, and when he looks at me, I will take a step backwards. Using the same principles, I will invite him into my space and reward him with softly spoken praise, gently rubbing his chest or shoulder, nose, whatever, each time he comes a little closer. Next, I'll alternate pushing him away with the "upright, tough posture", and alternately inviting him to follow by softening and lowering my focus. If you're having trouble with the posturing, exaggerate each until you get more consistent and fluid in your expression.
Now, what does all that have to do with crossing bridges? Everything. You have no idea whether you trust someone until you have shared some form of communication. You can shout, "Because I said so!" at a family member all day, but until you actually communicate sensibly and get a feel for each other, he or she is not going to blindly follow your orders; and that is perfectly reasonable on his part.
Once you have started building a good foundation of mutual respect and communication, you can ask for bigger and greater things. Remember, the relationship comes first. If you take the time to develop that trust, there will be little your animal won't do for you.
Now that you have your animal responsive and attentive to you, it's time to make things more interesting. If you have a tarp (less than $5 at Wal-Mart or any hardware store) you can use it as an introduction to bridge-work. It's important to always introduce scary objects in a non-threatening manner. With your horse or mule on a 15-20 ft lead, hold the tarp's edge and begin walking backwards, away from him. The tarp will drag on the ground (between you) and he may be frightened of it, but he will follow it once he realizes it is moving away from him. Allow him to "chase" it for as long as it takes for him to show signs of relaxing. When he lowers his head, licks his lips and his body language softens, you can drop the tarp on the ground and ask him to come closer. At first he may raise his head in alarm and may even snort at the tarp. If he's really upset, just pick up the tarp and resume walking with it, allowing him to follow it until he relaxes again. Do not rush this process. Allow him time to understand that he can be curious and interested in the tarp without it coming after him. These early lessons are important because the goal is NOT about having him walk on the tarp, but rather to teach him that he can trust you not to chase him with scary objects, that he can safely check them out without you getting mad at him, and that being scared is not a reason to run away. It is also about learning that he has to do what you ask, even though it may be frightening, because you will only keep quietly insisting until he does. These are very important lessons that once learned, will affect how he responds to you and scary situations for the rest of your lives together. If you grab that tarp up and go after him with it, you've just taught him not only to fear you and it, but that you are unpredictable and dangerous and that he should never trust you - lessons not conducive to a good, working relationship.
Once he is willing to approach the tarp, let him stand as close to it as he is comfortable. Ask gently but firmly with the lead for him to take a step closer. If he pulls or wiggles around, keep a firm grip on the rope but don't jerk or act aggressive, and don't let go. Always try to release pressure only when he is giving to you. If he is jumping around and being silly, hold the pressure until he gives in some way, releasing immediately the moment he even leans toward the tarp. Allow him to stand quietly for a few moments before once again asking him to take another step. Each time he argues just keep holding onto the rope until he softens and gives. When he gives, instantly release and soften your body language, tell him "Good boy!" and give him a rub. It doesn't take long for most to figure it out. If he walks over it quickly and jumps clear the first time, so be it. At least he did what you asked. Reward him with a rub and then take him back around and ask him to cross it again. Maybe this time he'll try to jump it. No big deal, just reassure him, and ask him to approach again. Make sure the tarp is unfolded and lying flat the first time you do this exercise, but later you can leave it wadded up a bit. The important thing is to reward any effort in the right direction, and not to reward silliness. Never try to punish him for being afraid, you'll only make things worse and he'll think you don't understand his point of view - and that will make him not trust you. If you show him that you understand his fear, and gently but firmly insist he do as you ask anyway, he'll soon learn that it's safe to follow you, that you are trustworthy and brave and that with you, he can be brave, too.
Once you've got him following you willingly over the tarp, try touching him with it or dragging it behind him. (Stay out of kicking range just in case!) Again, take each step slowly and don't assume that just because he is comfortable with one exercise that he'll be instantly comfortable with another. Do each one as if it is a completely new thing, because to him, it is. Remember, it's not about the tarp; it's about building trust and respect between you. It's about making mutual trust and respect a habit. Once he knows what to expect from you in lots of different scary situations, he'll become more and more comfortable in the knowledge that you are a trustworthy leader who can be trusted to get you both through any situation safely. With each challenge successfully met and handled, your relationship will grow until there is nothing your animal wouldn't do for you, and that, my friends, is a beautiful and precious thing.