Ive both Sold and purchased bikes privately, as for buying I have paid cash on collection, I always have a HPI check completed and pay the extra for all the possible checks, they will also guarantee the information provided. I had one once done for a bike at a dealers and it showed that finance was outstanding.
I always check the bike over, start from cold to see if there are any strange sounds, check all the fairing and look at the inside of the fairing for marks of repair. check wheel rims for marks, move wheels side to side for bearing play. check everything works as it should. I always buy from the owners house. If its a meet away from a home address then i have some reservations, i always take someone with me.
As for selling private, I'm happy that my house and garage are secure, i never give the house number just a post code then wait until they call me when they are on the road and direct them in to where I live. This way they do not have my address to steal the bike, I will not deal with a with held number phone call either. when the buyer arrives i show them round the bike then allow them to have a thorough look round and check the bike over, they can view all the documents and complete any checks they like.
If they some one views the bike and i don't feel happy i will take a picture of them.