I have done many Nitro finishes and re-fins...
First, a few questions:
1) The Fender body - what is the year and the place of origin? I had an early 90's MIJ P-bass that had a polyESTER finish that was a nightmare to remove (needed a heat gun). Some MIA fenders have a polyURETHANE finish that can be removed with chemicals.
2) While I am all for doing a refin for aesthetic reasons, I have to admit that I have found almost no difference in tone between the poly and the nitro finishes (the bass sounded the same after the refin as it did before).
You will have a million vintage snobs (not that there's anything wrong with that) tell you that there is a difference in tone between a poly and a nitro finish. That's only partially true - after many years of use, there MAY be a difference in tone as the nitro allows the wood to dry more with time; unlike a poly finish which encases the body in plastic and keeps the moisture pretty much sealed in the wood.
Now, all that aside - I recommend you do it yourself. It takes patience and some time (about a month), but you will 1) save ALOT of money and 2) have the satisfaction of knowing you refinished the bass yourself.
This guy is the only guy I know of that sells nitro in aerosol cans (they work well, I have used them a million times):
http://www.reranch.com/
READ EVERYTHING ON HIS WEBSITE - it's loaded with information.
Don't send him e-mails with questions as he will not respond. However, once I got two cans that had no pigment in the lacquer - he mailed me replacements without any question. Read/post on his forum if you have questions.
I am assuming that you will be doing a poly strip - in my experience, the chemical stuff is nasty...it melts the finish into this ugly goo that you have to scrape off of the body. A heat gun is easier (you can get one from Home Depot for about $20) but there are considerations - the poly will flake and pop off like popcorn and the smell is toxic - so don't inhale it, do the stripping in a well ventilated area (outdoors is best) and take breaks every 30 seconds or so. Next, you can actually scorch the wood under the finish if you hold the heat gun in one position too long...since you are doing a solid finish, this really is not an issue, but be aware.
After the stripping is done, I would give the body a light sanding with 220 sandpaper - you just want to remove any shiny spots, but be careful not to sand grooves/divots into the wood.
Things to order from reranch:
Sanding sealer (1 can)
Primer (1 can - this really is not required, but using it will help ensure you get good results)
Olympic white (1 can should be enough)
Clear coat (2 cans)
the sand paper package (I have never seen grit above 400 anywhere - his goes up to 2000 grit!)
the 3M polish.
Good luck