I use two overdrive pedals on my board. My favorite so far is is the Barber 1/2 Gainer. It's a guitar overdrive, but it has trim pots inside that you can tweak to make it a really good bass pedal. It's basically two of the Barber LTD's in one pedal. Here's a clip of the Barber Silver LTD, very close to one of the sounds you can get with the 1/2 Gainer by tweaking the trim pots: https://www.youtube.com/watch?v=RV2Sa-qo7YY
The other overdrive I use is the Okko Basstard. I use it alone for a heavy overdrive and I use it with the 1/2 Gainer for a fuzzy over-overdrive that I can do some feedback with if I crank the gain on my amp and push my headstock against the wall (1/2 Gainer -> Basstard): https://www.youtube.com/watch?v=E8u_OcH4MUQ
The other overdrive I use is the Okko Basstard. I use it alone for a heavy overdrive and I use it with the 1/2 Gainer for a fuzzy over-overdrive that I can do some feedback with if I crank the gain on my amp and push my headstock against the wall (1/2 Gainer -> Basstard): https://www.youtube.com/watch?v=E8u_OcH4MUQ