I would highly caution you against trying to get a girlfriend who "doesn't really like biking" to start riding. Seriously, you are entering rough waters for the relationship.

Having been through this both with friends who don't ride and a girlfriend who had been off the bike for almost 2 years after she was hit by a car on her hybrid, start with a cruiser. Keep an eye on CL over the next few months and see if you can find an old Raleigh 3-speed, or really any classic cruiser. They have a killer look, and they're super low pressure for a non-cyclist because you can't go that fast, it feels just like sitting in a chair because you're so upright, and you still look cool doing it. Also, you can get a great bike on CL for $75; a small fraction of what you'll pay for a new bike, but you can still probably flip it for profit.