I think bass distortion is best either with a blend knob, or two amps with one running clean.
Also, don't feel limited to "bass" pedals. Plenty of good thick fuzz, OD, and distortion pedals work great with bass, particularly the ones with a blend, and good EQ control.
The Game Changer Plasma Pedal (not the 3rd Man version), and Valco KGB Fuzz are sick with bass. The Plasma has a blend knob that helps the thump stay intact, where the KGB has both a blend slider, and a dry out so a clean signal can be sent to one amp, and the fuzz signal to another. They have the KGB Distortion which carries the same features. BTW KGB stands for Keyboard, Guitar, and Bass.