If the BB has not indicated any action, then:
Button acted out of turn and may be penalized at the end of the hand, but his hand is still live.
BB has the option now to check, bet, fold.
If BB calls (n/a), folds (n/a), or checks, then Button's out of turn check is binding and must check behind.
If BB bets or raises, then the out of turn action is not binding, and is allowed to call, raise, or fold.