I did it to one of my teles. I used a B5 model Bigsby with a Gibson Tune-O-matic bridge. I had intended on using one of the one-piece Bigsby/Tele bridges, but a tech whom I trust said they didn't stay in tune as well as the B5/Tune-O-Matic.
It stayed in tune pretty good as long as you kept everything well-lubricated. (saddles, nut slots, pivot points)
Notice I'm using the past tense....I ended up taking it off. When I installed the Tune-O-Matic, I had to shim the neck a little to compensate for the height of the bridge. This, seemed to cause the guitar to lose a bit of sustain. (Perhaps the fact that the strings no longer loaded throught the body contributed to this as well.) The guitar also had a little more high-end snap. (This part I liked).
Now I see Bigsby is making an adapter kit for teles. It includes a B50 vibrato unit (similar to a B5), a plate for mounting the bridge pickup, and a low profile bridge. I ordered the bridge and the plate, because I really want to give the guitar another chance with the Bigsby. When it arrives and I get it set up, I'll report back.
I agree with purpletele about not doing this mod to a guitar that you absolutely love as-is, as it is a pretty drastic mod. But, a Bigsby on a tele can be soooooooooooo much fun.
Later...