I received a payment of $3000 for freelance work in December. I didn't
cash the check until January, and when I did, it bounced. So my
question is, do I still owe 2005 taxes on a payment that wasn't good?

Cash flow method of accounting records payments when you "receive"
them. If you recorded the payment as income in 2005 when you got the
check, you will be taxed on it; you will have to make an adjusting
entry in 2006 and decrease your income by the same amount. If you
didn't record the payment until you deposited (cashed) the check in
2006, all the accounting will occur in 2006.

This is the reason I close the books in mid-December.