I'm considering putting radiant heat in my bath since I've got it down to the bare bones for a remodel. I've read that each square foot of mat draws .1 amp. I'll be installing approximately 12 square feet of mat, equaling 1.2 amps. Can I tap into an existing circuit for this little of a draw?

Follow the manufacturers installation instructions.

Wow! That sounds like too much. What brand are you using? Most of them (Including Suntouch) pull 1 amp per 10 square feet. 12 watts per square foot.
If you tap into a non GFI circuit, (No GFI's whatsoever!) like a light circuit, this can be acceptable.