It's very, very common in colloquial language. Bychom is on its slow way to oblivion, though it's still the only correct form in Standard Czech. I would not recommend using bysme in writing and in formal speech. In spoken informal language...it's, well, up to you. Some people might perceive you as uneducated or (almost insultingly) sloppy.

Personally, it makes me cringe everytime I hear it though I use it all the time when I am not paying attention to what I am saying...