Hi, Angie, and welcome.
My first question for you is this: Are YOU ready to consider a new relationship so soon after the end of a three-year relationship? How do YOU feel about this - not just him, but about the situation?
I'd tread carefully with this guy...something doesn't "smell" right to me...a genuinely interested guy doesn't sleep with a woman and then say, "I'll see you around, maybe." It seems pretty non-commital, in my opinion. Someone who knows what they want is not non-commital, even if they're attempting to play it cool.
I suggest you back off a little and see what happens. Remember - he can only see you as a "booty call" if you let him.