DA should have enough horsepower if you go fine enough with the sandpaper. Porter Cable 7424 is probably the de facto standard, and is dirt cheap now that the XP version is in ready supply. There are as many brands of pads and compounds/polishes as there are Jazz bass designers, so I hesitate to recommend. I will tell you that I lean toward Lake Country pads (the smaller the better - 4" and even 3.5" are terrific for projects like this) and Meguiar's polishes...although Menzerna is another staple on the shelf. FWIW, auto detailing sites, a la
www.autopia.org are great resources for finding deals on this type of stuff. For what you're doing, I'd guess you'd be looking at an investment of $150...possibly a bit more, which would cover sandpaper, the buffer, pads, and polish. Expensive, for sure, but if you plan to do any finish correction in the future...on basses or cars...you'll certainly see some ROI.
FWIW...and I bow to others with more sanding experience...I'll offer how I'd likely approach this. If you can work down to 3000-grit wetsanding, I'd suspect that the PC, with an LC orange pad and Meguiar's #105, would do the heavy work. You can then jewel the finish with a white pad and Meg's #205. If you're going this far, you may as well protect the finish. I recommend a good automotive polymer sealant. Good luck!