- Strings don't break, or go out of tune easily, unless a guitar is poorly set up.
- If something like that happens frequently to a player who's been performing for more than a month, it's because he wants it to.
- If you wanna do extreme things with any kind of whammy bar, you'd better have your axe(s) set up and maintained by someone who knows what they're doing.
Bottom line: If you really want to put a Bigsby on your Tele, then that's what you're gonna do. Just be aware that there's a price to pay in terms of tuning stability, and you're gonna need two guitars and a backstage tech, unless you're prepared to spend some time tuning between songs.
And your line of patter has to be something wonderful to pull that off without pissing off an audience!