Go to the lycra style club rides in whatever you want to wear and on whatever bike you want to ride, as long as you can keep up with your group, I did this when I started to mountain bike. I would drive my beat up car to the meetup point with the dismantled jamis inside my trunk, change into a sports t-shirt, cargo shorts and running shoes, then ride with these people in team gear on some really nice bikes. I probably looked like the really odd one out but I could keep up with the slower group (didn't know how to shift gears, so I just didn't) which always consisted of a few ladies who just wanted to have a fun ride, we talked while riding all the time. Don't forget the valuable information you can also give/get from riding with the real hardcore cyclists too, even the most seasoned cyclist has new things to learn about biking.

If this doesn't work for you, craigslist never fails. I've posted about playing tennis/rugby/soccer/mtb trail introductions and have met some really cool people who just want to enjoy a pastime and go on with life, no strings attached. Suggest a destination or loop ride on the activities page and see who bites. No scary weirdos so far