"I" day isn't the deciding factor. The day AFTER "I" day is the key. The day after "I", you take your "OATH". If you make it to that day, then if you get medically turned back any time during BCT, you automatically get your slot back next year. "Assuming the medical condition that got you turned back has been resolved".
If you DON'T make it to the 2nd day and take your oath; e.g. a person fell OFF the bus on the first day, messed up their knee, and got sent home... Then you have to start the ENTIRE PROCESS OVER AGAIN for next year. "Sucks, doesn't it". DON'T FALL OFF THE BUS!!!!
To answer the other part of the question: The air force will pay for your trip back home if you get turned back. Hope this helps.... mike....