to have a shot at something = to have a very good chance of achieving something
You don't have a shot with that guy. He's far too good for you.
Do you think I have a shot with that girl?
I wonder if there's a good shot with that hot lady there.
The point is, if you have a shot, then it's your call.
It's your call = up to you to do something, in this case go up and talk to the girl/guy
At least that is how I imagine the context here.