I've never really used the thumb for this technique, but if you want to try it out, rest your hand behind the bridge of the guitar for leverage and then slap the bass strings with the side of your thumb.

The problem with doing this on an acoustic guitar is that back by the bridge the strings are real "stiff", or don't have a lot of give, and you won't be able to get much sound out of it. You can try slapping the strings with your hand resting in front of the bridge and further forward, but I don't think you'll be able to get the right sound out of it without the proper leverage.

I think practicing the two finger slap would be a better way to get the sound you're looking for. I've been doing it for while and can do it almost second-nature in the middle of a song. It just takes pratice.