If you can be Dutch booked about probabilities asked in close sequence, where you gain no new information except that a question was asked, I'd think that reflects a considerable failure of rationality. There are grounds to reject "temporal Dutch book arguments", but this isn't one; the time and the "new information" should both be negligible.

To put it differently, if you have no information about what beads are in the jar, then you have even less information about why Omega wants to know your probabilities for the sorts of beads in the jar. Omega is a weird dude. Omega asking you a question does not mean what it means when a human asks you the same question.