I agree with Ladder13! He goes one step further than me- I copy down the information from the purchaser's DL and put that at the top of the BOS also listing the date, Make/Model/Serial# of the firearm.
As for what is legal, I cannot say how your state may differ but in mine, where there is no local firearm registration like NY and NJ, we go by Federal law and there is no paperwork of any kind required for a private party firearms sale. The only reason I insist on the record I mentioned is for covering my own behind!
And I cover my behind because of this scenario: if a firearm is found at a crime scene- if necessary the authorities go to the manufacturer and, based upon the serial number, the manufacturer tells them which distributer/wholesaler they sold it to. Then the authorities ask the distributer what FFL dealer they sold it to and when asked the dealer tells the authorities which individual consumer they sold it to.
Presuming I was the individual who purchased the firearm new, that would then bring the authorites to my door at which time I would produce the BOS and suggest they speak with that individual who purchased the firearm from me. Should the authorities then go speak with that individual and they inform the autorities that they sold it and kept no records (because no records are required to be kept for a private party sale in much of the US) then the authorites may need to follow other leads to try and determine who used the firearm to commit the crime.
If you like, you may always go to a Gunshop or FFL dealer and have them log the firearm into their boundbook from you and log it out to the new purchaser. In my experience, that only costs $25 to $35 to do but I still prefer to do it the way Ladder13 mentioned.
Actually, in a perfect world, I prefer to never sell any of my firearms!!
~Harvester