1. "Do you happen to know what a doodlebug is?" - note the order Gamer.
2. "Do you know what a doodlebug is?"
I don't see the one as being more or less polite than the other, except that 2 is perhaps more direct and 1. more suitable to suggest sensitivity to the fact that you may be interrupting the other person.
Apart from that, 1. suggests that you think the person is less likely to know than 2, that the knowledge in question more obscure, perhaps.