The cap does two things. A pickup's frequency response starts with a gentle bass rolloff, and then is fairly flat, until the resonant peak of the pickup. Here there is a steep peak, followed by a pretty rapid high end rolloff.
The resonant peak of a pickup is largely responsible for the characteristic tone of a pickup. The peak for bass pickups is somewhere between 1.5k and 6k...usually around 4-6k.
A cap will move the resonant peak lower which will also lower where the treble rolloff starts. The typical caps used in a bass are between .022uf and .1uf with .047uF being very common. These have too much of a sledgehammer effect for me, moving the peak too low, and making the tone too muddy.
With smaller caps, things can really get interesting. Smaller caps will move the peak more into the midrange, and leave enough range to maintain some clarity.
The Tonestyler does this, using a sequence of small to larger caps where you can clearly hear the movement of the resonant peak.
If you have a switch picking two caps, try one at .047uf, which is pretty standard, and for the other try .01uF. The .01uF will make you think you have a different pickup. The tone will get punchier, not muddier.
Or replace the tone control with a 6 position switch, leave the top terminal open (bypassed) and then wire 5 different caps on the other positions. I'd start with 333pF or 470pf, and then increase up to .022uF or .047uF. (actually, I'd probably to 333pf to .01uF.)
There are lots of things that affect a pickup's resonant peak. The size of the volume control for instance. A larger pot will smooth the peak, while a smaller pot will make it more prominent. Caps also have resistance and the resistance of a cap will change tone. A high resistance cap will sound different than a low resistance cap, taking two different caps of the same capacitance but different construction.