Interesting question.

I guess it depends on how the law looks at the transaction(s).

The feds would say that you are responsible for the profit you made during the deal but is this one deal or two? When I transfer ownership to BJ is that the end of one deal and when I have to "Buy it back" is that a second deal?

An important thing to consider s that it is against federal law for you or your agent to bid on items that you own and are being auctioned. It's called Shill Bidding. The whole purpose of you signing ownership to Barret Jackson is so you can legally bid on it since you do not own it anymore. The fact you get a taste of the profits for Barret Jackson selling THEIR car that YOU USED TO OWN smacks of Shill bidding but apparently isn't considered such or somebody would have pressed charges for it by now. Imagine how you would feel when you offer $50,000 for a car and end up in a two person bidding frenzy and end up paying 100K for that car, only to find out the other person was going to profit off you paying more for the car.

So I figure that

Scenario #1 If I sell a car to an "Other guy" and he titles it and declares he paid $X then I am on the hook for the sales tax. At that point I no longer own the car. If I buy it back and re-title it in my name the "Other Guy" he is on the hook for sales tax also, and I own the car again. We both pay sales tax.

Scenario #2 If I sell a car to an "Other guy" and he returns it to me for a different price, but the title isn't transferred then I could try to squeak by without paying taxes because I never stopped owning the car. (I bet the state/feds would say differently)

Now replace the other guy in the above 2 scenario's with Barret Jackson.

Scenario #1 Sales tax is paid twice.
Scenario #2 Is shill bidding because I own the car I am bidding on.

My guess is that you pay sales tax on when you sell it to Barrett Jackson and they pay sales tax when they sell it to you on the auction block, and then you pay income tax on the amount of profit you made on the whole deal. I'm sure BJ's fees more than cover them paying sales tax and cut into your money accordingly.

Still I am not only speculating.