Most horses are afraid to cross bridges…initially. Horses are naturally wary about anything that might trap their feet. A prey animal in nature doesn’t get a second chance to make a judgment error.
You don’t necessarily need a bridge to prepare for a bridge on the trail. Practice crossing lots of different things. Plywood, a tarp, a stall mat, a mud puddle. Carefully expose your horse to scarier things than you’ll encounter on the trail. My motto is ‘Overprepare, and then go with the flow!’ Just make sure your obstacles aren’t trappy. Particle board, for example, will break. If your horse’s legs get tangled, you’ll withdraw any training deposits you’ve invested.
Begin gradually, practicing crossing the width of an obstacle before its length. If your horse is quite fearful, start the process unmounted. You may even wish to sprinkle a food reward on each new crossing challenge. A powerful motivator, food links something scary with something pleasant.