I also gave a local person bluebird check (preauthorized) and BB emailed me when that check was cashed. So I like BB check better than usual billpay, because it's hard to find out whether they have deposited/cashed it or not from the bank billpay.
让房东use BOA银行 ATM to deposit. If ATM accepts the check and showing correct dollar amount, the deposit is successful. If after the deposit, BOA cannot get money from BB, it will show as returned check and charge a fee from 房东, and let 房东 show you the letter of return check charge, so you can argue with BB