I haven't tested this out yet, but can't you close the bingo UI, reopen it, and instantly get your number? I know that worked for the Cat Marble event.
nah I tried closing it... didn't seem to wanna close :P the X greys out as soon and you click spin
Also did anyone else not get their 5 'daily' coins for today? I stayed logged in overnight and have relogged and cc'd and don't recall ever getting those 5 bonus coins