When I have conducted private sales in the past I have ALWAYS written a bill of sale.
One line I have included is this:
"Is there ANY reason that you are not lawfully able to purchase/own a firearm?"
I have the purchaser initial and or sign next to it.

This shows that you, the seller has taken reasonable means to ensure that you are not selling a firearm to a "Prohibited Person".

It will absolve you of culpability if in fact the purchaser is unable to lawfully own a firearm.
I also include the date and time of the transaction.

A bill of sale just makes good sense. It gives you a bit of CYA if the purchaser decides to make poor choices with the firearm YOU sold them.