This is the way to do it. ^^ I've bought and sold lots of guns in the parking lots of McDonald's, banks, Academy, Walmart, even the local PD parking lot, right in front. What better place?
As long as a FTF sale is legal in your area, and I agree, find out, all you need to do, at least in Texas, is to not have reason to believe the buyer is a prohibited person, and you're good to go. Ask a few questions about the guns he has, his favorite place to shoot, just enough small talk to be reasonably sure he's not buying a gun to go and hold up the local stop-n-rob, and take his money.
A bill of sale is really useless. How do you know the buyer is who he says he is? If he's a prohibited person and he agrees to sign a BOS, how do you know he doesn't have fake ID? And how does that protect you ten years later anyway? All you have to do is tell any LEO you sold the gun way back when, you don't know who bought the gun because you're not a dealer and federal law doesn't require you to do a 4473. End of story.
By the way, I don't ask for nor give bills of sale. If someone insists that I sign one, the deal's off. I haven't seen a gun yet that I couldn't buy elsewhere maybe for less anyway. As long as the buyer had what appears to be a valid in-state DL or CHL, I do the deal.