if you sell the bike privately and then go buy another bike, you will have to pay sales tax on the full amount of the new bike. if you trade in your old bike, you don't pay sales tax on the amount of the trade in value. so ask yourself if it's worth the hassle of selling it privately as compared to the tax savings of just trading it in. here in texas the tax rate is 6.25%, so if you figure that on a $7,000 trade in, you'll save $437.50 on sales tax. you'd have to get at least $7,500 selling it privately to make it worth while, but then figure in the time to do it, people saying they're coming to look at it and never show up, wanting you to finance it, hold it for 2 weeks till they get the money together, and then you never hear from them again, joy riders, etc etc.
good luck.