Did you come up with anything? Occasionally when I'm driving or something I think about it. A distortion pedal might do it - I like the Fulltone Bass Drive - it sounds great, and gives you two levels of distortion. They aren't cheap though!
But then I start to think, maybe a multi-effects unit would be better - doesn't have to be super-fancy, but you could have access to a lot more sounds for variety, like flanger, distortion, delay (ideally - for example, I don't think the Bass POD has any), etc. But I'm not a multi-effects kind of guy, so I can't really help much there...