I had a difficult time getting bridges to work as well. In the one depicted below, I graded my highway approaches at around 300 meters height on both sides (50m above sea level). It doesn't have to be at 300m height per say, but the approaches should be at the roughly the same height on both sides of the river, or other area being crossed. Normally having equal highway approach heights was good enough to make the bridge build, but after installing NAM, this was no longer sufficient to make the bridge build happen, and id usually get an error. Now, since NAM, the bridge building requires a bit more precision in terraforming, but once you get the hang of it, its not too bad. So, after grading the approaches at an equal level on both sides of the river (using the 300m height in this case), I then laid a level pad of 3 tiles x 4 tiles, just above sea level, at about 253m, or 3m above water level (standard sea level is 250m in SimCity 4 ) on each side of the river, just at the end of the approach. You will note in the final picture, that once the bridge builds, it fills in the earth over top of these pads, so they appear to "disappear" once the bridge is built.
PS, i also use the SimCity 4 extra cheats plugin for precise height measurements: Once installed, press CTRL + X and enter "terrainquery" into the box and press enter. I'd never be without it now!
