It may be that your B string isn't centered over the poles in the pickup.
Here's a little test, (someone else may have a better way to do this), - take a ferrous object (in other words, something that contains a lot of iron), like a metal paper clip. Run it over your pickup area where the B string would normally be and see where the area of strongest magnetism is.
If that area of strong, magnetic, pull and the area where your B string normally falls are clearly different, your pickup is probably only "picking up" the "signal/info" that your B string is giving it at the furthest edge of it's vibration. In other words, your pickup may be only be "seeing" just some of the vibration of the B string because it travels outside what the narrow vibrational travel that the pickup can "see."
That's one of the reasons I was happy to get a bridge that can be adjusted to center the strings over a pickup's poles.
If you aren't intimidated by very techie info about such things, (as I am), you might give this place a look -
http://www.till.com/articles/PickupResponse/index.html#vibratingstring
Other than that, make sure your B string's saddle is adjusted to where the B string can vibrate/travel pretty well. We all like a taut B, but those babies do need some room to roam.
