Hi Chuck,
There are various ways to do a drop off and it can be done with various instruments either in the studio or live.
I always believe getting the actual source (sound/technique) right would be ideal though I'm not entirely/exactly sure what type of Bass Drop you want so I'm going to throw a few ideas out there for you ;)
I think it's also a matter of a performance technique to begin with and arranged where it fits; to pause. This will make the Bass Drop stand out way much better.
Can get that effect 'LIVE' on a guitar to bend the pitch down (trem arm or heal rest). But doing this on bass won't be so easy, doing on drums 'LIVE' would require a sample trigger 'pad' (electronic kit pad) loaded with the right sound that includes the drop off. Or unless the real skins and shells are incredibly flexible enough but I doubt a traditional drum kit will cut it LOL!!
For in the studio; Start with a short sample and add pitch-bend (down) at the tail end using a pitch controller.
If it's a real bass, drop a snippet (short segment) into a sampler and then you can control the technique from there. Otherwise, a really good pitch-tool and automation to control the drop off.
Try Melodyne Editor or V.Vocal pitch-curve, curving the pitch down, way down for the tail end, it might work? though how well I'm not sure?.
I prefer the, get it done at the source, that way it can be performed 'LIVE'! The easiest way is to assign the sample to a trigger pad.
Anyway, it wouldn't hurt experimenting. Good luck! -