It's complicated. You are taxed on the "fair market value" of the item. FMV is what a willing buyer will pay a willing seller in an open sale (not forced).
If this motorcycle normally sells new at a dealer for $22,000, that's probably the taxable FMV. If you sold it used, and you got less than full price because you rode it a little bit, and you aren't a dealer, and don't have a warranty, etc., then the taxable value of the prize was still $22,000.
However, if the contest organizers gave you the option of taking the motorcycle or cash and you chose cash, then the cash you took is the value of the prize.
If the motorcycle's list price is $22,000, but dealers usually sell it for less (due to discounts, rebates, and so on), then the lower value may be the true FMV. The fact that the dealer bought it for less (because they want to make a profit when they resell it) is less important than what that dealer or a similar dealer actually charges for a bike in the same condition that you received it (new, never ridden, etc.). You're always going to take a loss when you sell or trade in something used, even if it is barely used.
Lastly, if you got a 1099-MISC for $22,000 and report anything less, you can expect to get a letter from the IRS and you will be asked to provide proof of how you determined that the fair market value was less than on the 1099.
There is a tax court case where a customer won a $5000 necklace from a famous department store, and they gave him a 1099-MISC for $5000. He had it appraised by an independent jeweler for $1200, and reported that on his tax return. At audit, he was able to prove that $5000 was the department store's "comparison price" and the necklace was always "on sale" for between $1700 and $1999. The Tax Court ruled the taxable value of the prize was $1700, since that was the price the department store usually sold it for in open sales with willing buyers.
