We recently sold our RV and explored the process although we finally traded due to sales tax credit on a trade in our state. The process is not all that difficult. Talk to your bank. they can set up an escrow acct for you if you are paying cash. They then can safely set up the details of title, etc with the other parties lien holder. You and the other party are out of the picture.
All you have to do is find the RV you want and agree on a price and get a bill of sale and insurance. Do check with the state you will register the RV in as to how sales tax is handled. Here in TN it is 7.5 on the entire purchase price minus any trade in allowed. Thus a dealer buy can be attractive as buying privately would forfeit the sales tax credit of a trade.
Your state is likely different so check it out. good luck.