Chiggy:
I think you should talk with some local riggers who might help you with the lift. A good share of what you might do will depend on the lifting equipment they have available. Alternatively, what you can do given the strength and weight of the bridge might dictate that some methods or equipment would not work.
What does the bridge weigh and how wide is it. Obviously, you will have to do some analysis of the existing structure to see what will work. You might lift from above or along side of joints A, but you must keep the bearing points clear so you can set the bridge down on the abutment bearing points. You would probably have to design some removable lifting fixtures to do this. Lifting at four points, with cross beams, under outer joints B or joints C, might be easier to design and from the rigging equipment standpoint. You might have a crane at one abutment, with sufficient reach and cap’y., and slide the entire truss across the creek to that crane position. The sliding end might be done on rails and rollers, and can be lifted and positioned a little with a front end loader, or smaller crane without the reach, or some such.