I rented a Kia Soul this past summer and it is quite a nice car for an inexpensive car (start at $16k). Handled two bikes in the back, luggage and my two sons. I did remove the wheels from both bikes though. If just one bike it will fit in the back with the front wheel off and you'll have plenty of room to spare. Quite a peppy little car too and the gas mileage is good and is rated high by Consumer Reports and Car & Driver magazine. I'm thinking of buying one for myself when the time comes. Oh, and the OEM stereo isn't too bad either!
I highly recommend that you rent a few of the cars you're looking at first to get a better idea if they will do the job for you.