Interesting... the life progression for me was the opposite. Through my teen years,I thought I couldn't dance, and then by college, I decided maybe I could. I did a few modern and African dance classes for PE credit, and I participated in some folk dance groups. I definitely would not quit my day job to make a living from dancing, however I do love it (along with not being terribly 'good'). I'm firmly convinced that 'good' or 'bad' dancing is more about the dancer's attitude towards themselves as they dance. If the person is having fun and expressing their joy, it looks good regardless of whether they would win a contest.
By the way, not all dance styles involve moving the hips! For example, Israeli folk dancing focuses much more on moving the legs and feet, with almost no hip movement. If you do want to explore some other styles, try a Western or line dance group, or most kinds of European folk dancing. Yeah, you have to learn a series of steps, however that's part of the fun. Or you could go the psychotropic drug route, though I personally like being able to remember what I did... :)
ETA: I wasn't thinking of a formal class; more something along the lines of a dance club, like a line dance group which gets together once a week or once a month just to dance and have fun. They're informal and often offer some instruction for newcomers in the first hour or so. It's cheap and fun, and there should be no snootiness. Just a thought...