You are supposed to book bounceback before you check out of your room. I have read before of people calling shortly after checking out (like 2 days later) and being able to book it--but I'd plan to do it while I was there to be sure.
As for the refundable question--I'm not 100% sure of the restrictions there. I can tell you that a room-only reservation should be 100% refundable with no restrictions as long as you cancel/change more than 5 days before your new trip. A package deal is usually refundable up to 45 days of your date of travel, but there may be the issue of the "insurance" portion of the deposit not being refunded when you book a package.
Disney automatically adds in trip insurance for packages--so I'd be sure to check that if you are planning on trying for a
free dining bounceback. Hopefully someone else has the specific details.