The Toyota RAV4, 2001-2005, has rear seats that are easily removable (they unclick and remove in seconds), and enough floor-to-ceiling height to allow rolling two bikes inside without removing wheels. You just have to angle the bikes to get the bars and saddles thru the rear door opening, then turn the front wheel to rest in the rear passengers' footwells. Bungee-cord the bikes to the passenger ceiling grips, and you are ready to go. Still plenty of room to stow other gear around the bikes.

If you want to transport just one bike, you can leave the second rear seat in place. Works great.

I recommend the 2004 or 2005 model years, with the more powerful 4-cyl engine but same mpg rating. (I have the 2001 model, and with the lower horsepower it does not climb hills very well, if that is a consideration.)