Mike has sent a PM asking to help resolve the issue.
Note the disclaimer above: "My experience has been . . ." Obviously they don't treat everyone the way I've been treated. Mike's right that something odd is going on; I am hopeful that we can get this worked out.
The facts are pretty much as I stated above--the bike arrived damaged, I emailed immediately, and after a week, when they hadn't agreed to pick up the bike, I filed a dispute with my credit card. That afternoon, they agreed to pick up the bike. After they received the return, they emailed and said they couldn't issue a refund until I cancelled my dispute, which my credit card company advised me not to do.
Yesterday, I received a letter from my credit card stating that Bikesdirect claimed not to have received the return package. Both their own email and UPS confirm that it was delivered on November 13. The burden is now on me to prove that it was delivered, or my credit card will be charged for the purchase price of the bike, which arrived damaged and was returned to bikesdirect over a month ago.