The BP-100 is a very nasal, twangy sounding outdated pickup. Because of it's extremely close proximity to the strings, there is little to no "woody" sound in the equation.
I would seriously consider getting a better pickup.
For a nice fat Bluegrass sound I would recommend a Bassmax, or Underwood (using E side pickup only) which are both bridge wing pickups. The David Gage Realist is also very popular and picks up the sound under the bridge foot, which can sound very natural but can also have more feedback issues at higher volumes.
Do some reading on pickups here and it should help you make your decision.
I've played several basses with the BP-100 who sounded great amped. But then I've played basses who sounded just ok or even like crap with the fishman. You just have to try it - however do not miss to use a high imp buffer.
Sorry, but I've not found the Realist more to feedback than other PU:s at higher volumes. Again, it depends on a lot of different aspects.
My 2 cents is shop around and try as many basses, pu:s, strings, string heights etc as you can. If you find something that works for you, stick with that and sell the stuff that you don't need.