Yeah, if it were a regular thing then I can see how you might should consider an FFL.
But more to the point from the ATF:
https://www.atf.gov/file/58681/download
Again, stated as not a requirement but a suggested "best practice" to at least check ID.
"If you decide not to utilize the services of an FFL, examine the purchaser’s identification document to confirm that the person is a resident of your State"
Fact: a firearm bill of sale has never helped anyone, but it has put people in jail. You feel that you need to CYA because you lack knowledge and experience. Let go of your feelings! Don't be like them. Embrace logic and reason, do research, trust input from more experienced people.
Firearm bill of sale is FUDD nonsense, or "universal background check" treason. Step back from your ego and accept that you could be wrong. Then welcome to a bigger world.