I've done this going to Costa Rica...so here is my $0.02.

1. Overnight almost certainly means that your checked bags will only be checked to MIA. you will need to collect and re-check in the morning.

2. The Bahamas are not part of the United states. Therefore this is an international flight with the associated check in time requirements.

3. Coming back, assuming you do not have a very long or overnight connection, your bags will be tagged through to the final destination but you will still have to collect them in MIA, clear customs and then redeposit the bags with the airline.