I'm going to assume that pedals in bass world, aren't all that different from pedals in guitar world. If my assumption is correct... i would recommend avoiding anything that calls itself a "distortion" effect. Distortion is typically very non-organic, thin, and buzzy. Overdrive is typically more natural, and makes better use of the sonic spectrum. The problem is... many manufacturers make distortion pedals, and put the word "overdrive" on them (especially on the low end of the price spectrum). Your best bet is to try before you buy, unless you're already familiar with the manufacturer, it comes recommended by a friend who knows what you're looking for, or they do one helluva job of convincing you with their presentation, that theirs is a
true overdrive. Many valve units that claim to be overdrives, can sound buzzy and unnatural. They typically come loaded with a 12AX7 (ECC83), which frequently provides gritty "electric razor" tone. A guy over in the amp/preamp forum clued me in to the idea of swapping the stock 12AX7 for a quality 12AU7 for more clean boost before distortion, and a more natural and controllable distortion. I'm anxious to play around with that when I have a little play money in my pocket