Second time this week I'll say: It's not a bridge. (unless you're talking about the extremely obscure Bigsby bridge as seen on this old Les Paul. Hint. It's not the thing with the lever sticking out)
So after the pedantic asshole part of my reply I'll say that it totally depends on what you want from the guitar. The Bigsby will change the tone slightly. But don't believe that it's (a) extreme or (b) will make the tone worse. IMO it makes the guitar slightly twangier, but it's barely noticeable.
Also be aware that the Bigsby sound is not like a Stratocaster or a locking vibrato system. You dip only be a little over a half tone. The up side is that it creates the most lush vibrato sound you'll hear - especially on chords.
There is now a product for people who are unsure (chicken ? ) about whether they want to put screw holes in their guitar, called a Vibramate. It allows you to attach the Bigsby without any modifications. It does make the tailpiece stick out more, which is why I didn't bother with it. But it means you can try the tailpiece and then change back if you don't like it.
http://www.vibramate.com/index.php
You'll probably want the B30:
http://www.bigsby.com/vibe/products/vibratos/bigsby-b30/
It's the licensed version of the B3. No practical difference I'm sure. But it's cheaper. I bought a B7 rather than a B70 for my Les Paul, but only because I was putting it on a very expensive instrument.
Don'ts:
Don't get a roller-saddle bridge. The consensus is that they're a tone-suck and that your current bridge will work fine.
Don't blame the tuners or the vibrato tailpiece if it knocks your guitar out of tune. It'll be a badly cut nut, the saddles, or both. It's inexpensive to get the nut sorted out and smooth - with some graphite powder from a pencil to prevent strings sticking in the slots.
On a well setup guitar, a Bigsby will not cause you to go out of tune.
I bought mine from Stewart Macdonald. Try get in on a group order with other forum members to reduce shipping costs:
http://www.stewmac.com/
