For the BP-100 you need a first stage amplifier with a 10 MegOhms input. No power amp or combo amp has this, so you need a preamp with 10 MegOhms input impedance (Fishman or better HPFpre). This might remove a few resonant frequencies, but I'm afraid only some. At least as much important is the mounting (as Jake told you), since the disk must be fixed very well to the bridge and a plan bridge surface is very important for that.
But don't forget that a feedback loop includes speaker, room and bass, not only electronics. So the position of your speaker relative to the bass (distance, height, direction) is very important to avoid feedback. That may include being very carefully about your body/bass movements. Try to position your amp high, at least 1.5 meters from your bass pointing at the rib, not at the top or back of the bass. I think this might help more than a preamp (but the preamp gets you a better sound that you might want to have).
If this does not help, you should know, that a BP-100 only works on a few basses and that using effects might make the feedback situation worse (at least with those enhancing or adding frequncies like overdrive, fuzz etc.).
Some people glue the BP-100 to the bridge with epoxy and say this helps, but you should read about this in the archives before you decide to do this on your bass (you might not be able to remove the epoxy later...).
