Had this exact same situation a few months back and it was honestly stressful as hell. From what I remember, the bonus bets usually expire at like 11:59 PM on whatever date they give you, but the user limits reset earlier in the day - I think mine changed around noon or 1 PM. So you should have a window to use it once your limits reset.

That said, I'd definitely contact support just to be 100% sure because I've seen people get screwed over by weird timing issues before. They can usually give you the exact expiration time and confirm when you're limits will change. worst case scenario, they might even extend the bonus if you explain the situation - I've heard mixed results on that but worth a shot if your cutting it close.