I got a cheapy bike rack at the bike store I used for a couple of years .. Now my sons using it ... spent around $125.00 on it .. I'ce since got a new vehicle with a hitch and gone to a thule . ,, What ever you get putting a girls bike on a rack can be a PIA ... This bar you add to make it a boys is pretty cool and makes it easy ,, I used it a couple of years now .,. Swagman Bar Adapter Deluxe: Amazon.com: Sports & Outdoors
You need to be sure the rack you choose fits your car. A lot of cars withspoilers on the back can't take the strap on type racks. If you have a hitch on the Mazda that is the way to go.