When you run at full volume on a passive bass, essentially you're letting as much of the signal through as possible, as if there were no volume control at all and it's fine, your amp can handle it no problem.
Instruments with active EQ, however, have a EQ boost funtions which can dramatically increase the output of specific bands of frequencies and can sound unpleasant to the ear, I'm sure everyone has heard the Stringray all-on-full sound more than once. Some active circuits come with an output level - usually found on the circuit board, which can cut or boost the general output level of the active circuit by quite a lot. If you've ever heard someone move from active to passive mode with a huge drop in volume, that's what you're hearing.
Distortion isn't quite as desirable in bass as it is with guitar so decent bass amps, unlike guitar amps, generally have an input level control as well as an output level control as onboard active circuitry is quite normal in the world of bass and can accomodate passive and hotter active signals without distorting. The input level controls just how hot a signal is allowed into the preamp. Most amps will come with a clip light (or a needle on Ashdowns for example) where you can gauge when the preamp is starting to distort - as a rule of thumb I usually keep it just below the point of clipping.
If you're still worried you can lower your pickup down, away from the strings and it will result in a quieter output.