I looked into this recently for an upcoming job that had a bridge inspection requirement.
There are two types of courses that offer training to the National Bridge Inventory Standard (NBIS) by the Federal Highway Admin -- one lasts a couple of days and the other is a two-week course. The longer one is required in order to be an inspection team leader and is offered at one of the universities in New Mexico (January and May of every year, I believe.) The short course is offered in various places and times(you have apparently discovered the same information that I did (NHI).
Each state DOT is responsible for "certifying" (not sure that is the correct term?) Bridge Inspectors (more or less based on having successfully passed the course.) Some bridge inspection teams are comprised of State employees (in-house) and some contract out these professional services to a consultant.
Check with your state DOT to find out how it is done in your area; they should also be able to provide you with a list of what companies they hire (if contracted out.)
Hope that is the type of information that you are seeking. Good luck with your search.
In Florida there is a Certified Bridge Inspector program. I don't know exactly where but I do know You have to have 4 years underwater and 1 year topside inspection experience or have an engineering degree. Bolt Underwater Services in Pinellas Park, Fl. only does bridge inspections. They would know more about it. All bridges in Florida have to be inspected every 2 years. Lots of work.
The NHI underwater course is rarely offered. Usually, a state DOT or company has to sponsor it. You can call the NHI training director and ask what it would take to have them schedule a session. I think it's typically taught by some engineer-divers from a consulting engineering firm. Let me know if you can get one on the books.