Admittedly, moving water doesn't always seem like a place you'd seriously consider throwing finesse lures for bass, but don't forget that finesse presentations are always one of your options. The decision of whether or not to use light lines or smaller lures should be based on how to best get your lure to the fish with the most natural presentation. That's really the key to finesse fishing in current.
Of course, you can catch bass on spinnerbaits and even crankbaits in moving water, but these lures don't appear very natural. Bass have to be in an aggressive mood to hit them. If they're not, you'll do much better with finesse presentations. As I've said before, a lot of factors influence bass behavior, including fishing pressure, water clarity and the weather. Generally, it won't take you long to determine if bass are aggressive or not.
One of the most important factors about finesse fishing in current is learning to "read" the water. There are a lot of different patterns whenever you have moving water, but the three most important options in bass fishing are (1) the fast current itself (the main water flow), (2) the "seam" where that fast moving water slows its momentum along the line with calm water, and (3) the eddies behind some type of obstruction where the water is basically not moving. So, when I'm fishing in moving water, the first thing I have to determine is which of these three choices the bass are using, and two of my very first considerations are the season of the year — yes, "seasonal patterns" apply in current, too — and the actual mood of the bass.
Figuring out the basic location of the bass according to the season of the year is actually easier in current than on a wide open lake because the fish have those three basic options of current, seam, or eddy locations. Here are the basic guidelines I use for this, always remembering bass can and do change locations as conditions dictate.