I understand your worries about crossing the brigdes, it can be a nightmare. I have enough experience with them to have learned to be careful.
First; It is not always an option to let the dog swim across, even if he is used to swimming. The current can be strong, and there are often rocks in the river. He can panic, you can panic.
I have a 42 kilos dog, and we just crossed 8 brigdes when we crossed Hardangervidda some weeks ago. Some of them are easy. Wooden, solid brigdes that goes directly from the ground or a rock. Other brigdes have ladders og steep stairs to get up and down. Some have open patches in the beginning and end to avoid sheep and cattle to cross. All of this can be a challenge for a dog.
Here is what I do when I cross complicated bridges, usually suspension bridges:
I always bring a harness and 2 x 5 meters of rope. The harness is solid and for mushing. In a crisis I can haul him out of the water in it. I tie him up (important or he will try to cross after me), and cross over first with my and my dogs backpacks. Never let the dog wear a backpack when crossing suspension brigdes. They loose their balance. Then I go back and tie the rope to the harness properly. If it starts with a ladder you have no choice but to help him up. My dog tries to climb, and I help with the rear end. You should be able to lift your dog (consider it an excercise ).
When we cross I allow him 2-3 meters space and walk very carefully behind him. Let him have his pace. If he stops I talk calmly and command him forward. I make sure I don't rock the brigde. He might loose his balance. When he reaches the other side I go close so I control the way down. If it is a ladder I sort of lower him by the harness. Stairs he handles himself. The rope must be loose enough for him to have full freedom, but not so loose that he might get it around the feet. Don't pull the rope. If there are open patches on the brigde I can see he doesn't handle, I command either forward or jump.
If you take your time and let him find his way it is my experience that the dogs find it a bit exiting. Make sure he doesn't enter the brigde until you are ready. I once found my dog on his way up a ladder. He fell to the ground. Thank god no injury, but I've learned my lesson.
If your dog flat out refuses to enter the brigde, don't force him. Panic will for sure send him down the river. As a last resort you'll have to cross the river with him if possible, or carry him over the brigde. If you have to carry him, make sure you have a firm grip on the collar and harness so he doesn't start moving and you loose him.