I have an 86 Toyota Camry, which is about the size of a Corolla. It is a four door. I take the front wheel off and slide it in the back seat. It fits perfectly. The mtn bike fits, too. Just be sure to put a towel on the back seat. I always manage to get grease on the seat.
We just bought a 96 Honda Civic. We did not want a bike rack on the trunk so we had a welder make a hitch rack for it. Now we can use the hitch rack for the Jeep or the Honda.