Wanted to add: If the "Your checkered room and your velvet bow" is not an allusion to Alice and Wonderland as suggested (but I think it is also), then it's still alluding to some symbols that getting the girl he wants is just a fantasy. Her velvet bow may be a symbol that she is too good for him (or thinks she is), and the checkered room may be a reference to her playing games, or being hard to win, like a game of chess.
Wanted to add: If the "Your checkered room and your velvet bow" is not an allusion to Alice and Wonderland as suggested (but I think it is also), then it's still alluding to some symbols that getting the girl he wants is just a fantasy. Her velvet bow may be a symbol that she is too good for him (or thinks she is), and the checkered room may be a reference to her playing games, or being hard to win, like a game of chess.