Bronco Piccolo build
 

I'm in the process of turning a Squier Bronco into a piccolo bass. I'm pretty sure the stock pickup is straight from a Squier strat and I intend to replace it. What I'm wondering is whether to go with a brightish bass pickup (say single coil jazz) or a warmish guitar pickup (say an alnico humbucker). What do you guys think? Or is there a better option?

I had good luck with the GFS lipstick tube pickups. They're a guitar pickup but are full range so they'd work for your purpose.
Plus, they look really cool.

http://www.guitarfetish.com/GFS-Pro-Tube-Lipstick-Fits-Strat-CHROME-_c_188.html

I used one of the humbucker versions for a tele bass build a few years ago and it sounded great.