You want a bridge pickup that can go from jazz and funk to thrashmetal? I think that is asking too much. In a set that is somewhat possible, but with a single bridge HB it will be nigh impossible to get them all going good.
For starters bridge PUs are not exactly known for a good clean sounds. Parallel and split wiring can help, but still good cleans are ususally neck stuff. Just going by what has good cleans on the bridge one could suggest the Crawler, as it is nicely full, powerful, has great character and is very versatile. With the proper wiring you can take it from cleans to metal, however it is perhaps the least tight BKP (which does not exactly mean loose, still pretty good compared to other stuff out there, but it has a rather warm bottom end), so thrash and power metal would be somewhat of a stretch I think. It is however extremely versatile for all the other things, partially cause it splits better than anything else out there, huge bonus.
Alternatives could be the Abraxas, which is, to be quite general here, somewhat of a pumped up mule or toned down Crawler, depeding on how you look at it. Can handel the high gain easier as it is brighter and tighter compared to the Crawler.
I also always say that the oposite of a one trick pony is a Mule, as it really works with sooooo many things, but it might be a bit too low in output here, especially lacking power for splits which you could really use I think.
The Holydiver can also cross ones mind, as it also has rather good bridge cleans, but the voicing strickes me as too rock and metal for these here needs.
I would guess the Crawler or Abraxas would get you close, but keep in mind this is a pretty tall order here.
