Actually, I think if you are looking for an overall bigger sound, you need to figure out how to get a huge CLEAN sound first. A weak wimpy clean sound put through through tons of distortion, effects, and big amps is just going to sound like loud, fuzzed-out, effected, weak, wimpy tone. Some sort of pre-amp might be a good idea. Or even just an EQ pedal placed at the beginning of the signal chain. Of course, good pickups, beefier strings, and good right hand technique go a long way too.
I use my bass amp to take care of the low end (i cut the highs on the amp), and then I have a cable going from the tuner out of the bass amp into the input of a guitar combo (doesn't need to be big, 30 watts would be fine, as long as it can get a nice, clear, not-too-heavy, tube overdrive), I have the lows cut on the guitar combo so only the rich overtones are going through (the lows would just muddy it up). Doing this gets me much more of a big sound than just relying on an OD pedal through my bass amp alone.
Big doesn't = loud, and big doesn't = more distorted. Big = strong, rich, and punchy, no matter how loud or distorted it is. Start with a good, strong, fairly-clean tone, and then just add enough overdrive or distortion until it sounds right texturally in the context of the whole mix, making sure the distortion doesn't subtract from the bigness of the sound (a lot of distortions actually weaken the tone, they only superficially sound "heavier" because of the added noise and crunch). Then work on making it louder while maintaining the same balance and texture (usually turning the volume up changes those things).