I fish in my kayak almost exclusively at the bridges. It is illegal to tie to most bridges but my friend who taught me the technique never tied his skiff. I pitch soft plastics (finesse and bass assassins) as far under the bridge as possible. I'm always facing into the current. Count down your bait since most bass are well below the surface. You can experiment with varying your retrieve. I use powerpro and a 30 lb. mono leader. I have my drag set fairly tight to muscle the fish away from the bridge. Jighead weights vary from 3/8 to 3/4 ounce. Good Luck!
Oh yeah, if you're not getting hits after awhile, move around to another spot.