Even if you find something that works, like an adult-size "Tag-Along" or a suitable tandem, are you sure your girlfriend is willing to use it? Many people don't like hard physical activity under any circumstances and her refusal to ride may be the result of that attitude. Be sure it will be accepted before you spend any more time or money.
My wife never learned to ride a bike as a child and I made the mistake of trying to teach her when we were in our 40's. It didn't work and it would have been a ticket to divorce court if I had persisted. Teaching our teen age kids to drive was a piece of cake by comparison.