back when i was starting out, i was a big fan of those bass dirt pedals ... but a big lot of them sound good when you are alone but gets lost in a band setting (especially if the guitar player also has distortion) ... the only way i can compensate for the low end is adding lots of subs in my equation and well, that is too taxing for the cabinets.
i have owned (and sold): diezel dirty dawg, Boss Fender Bassman '59, Digitech Bad Monkey, Big Muff (american one), HBE Hematoma, and a Bootleg 2.0
what i noticed is that TS clones usually play well with bass because they dont mess with the low-end frequencies ... so for that, i recommend a digitech bad monkey as the cheapest "experiment" ... if it fits your band then good, if it sucks, i guess its easy to either sell it or just keep it around.
currently, i dont use any dirt pedals (or any pedals save for a redwitch moonphaser and a tuner), but i still do have the Bootleg Hizumi with me (i got it really cheap and selling it would only get me string money or something) ... here's what it sounds like:
the recording is terrible ... but well, you can still pretty make out what it will sound like in real life. i think some bassists might find a sound for it.