My band is playing a few songs where I'm going to have to pull out my 6 string (for the low B).  I really hating the feel of the B.  I have taper wound strings on it (DR Long Necks).  Wouldn't the narrow winding passing over the bridge serve to decrease the string tension?  I'm thinking that if I went to a non-tapered set, the tension would be higher and it wouldn't feel so floppy.  Thoughts?

Mike, the taper wound string just makes the string easier to intonate. You may want to use a heavier string to make the B string tighter.

Hmmm... I really hate heavy strings.  Maybe I'll try some Lo-Riders (the hex core is supposed to make the strings stiffer).

LoRiders are pretty stiff - it's what made me change back to HiBeams.

I just ordered a set of 125 Lo-Riders... I'll report back on my findings.  Back to my original question: it seems to me that the decreased mass at the anchor point (the bridge saddle) WOULD result in less tension.  But admittedly, the E string is also tapered and it feels about the same as my other LS basses.

I just got the strings (DR Lo Riders 30 - 125) and they are a definite improvement over the Hi Beams (from a B string perspective).  If you have a floppy B you might want to try these.