A big league contract doesn't solve the bonus money problem, that money still comes from the prospect payroll.
If you have any funds left from player payroll to transfer to prospect payroll you can do that. If you don't have the funds you can try to trade or waive one of your big league contracts (keeping in mind that you have to prorate the contract for however long into the season you are). And then transfer the freed up funds from Player to Prospect.