If you give a bonus on an interest bearing account you would need to give a 1099 INT.
I believe this is only true if the bonus meets the IRS definition of interest - meaning it has to be paid for opening, adding to, or maintaining an account. If the bonus is paid for signing up for direct deposit, online banking, debit card, etc., it wouldn't be interest and would be reported on a 1099-MISC if the aggregate amount is $600 or more.