Yeah I tipped over into my car the first time I got up on "Dotty" because the pad of my shorts snagged on the saddle and I freaked out thinking I was going to lose my shorts. As you said, Plop! Had a nice set of scars on my right calf from where they came down on the spokes of my back wheel. To this day, when I take her into the shop they remind me how a crashed that beauty within 5 seconds. BUT, about 6 weeks later I did ride my first charity ride, the Ride 26.2 with Donna here in Jacksonville. I am doing the TdC (51 miles) here on May 18 and if that goes well, I am going for the MS Tour to the Shore! (2 day St. Augustine, Daytona and back the next day).
You will be fine! As they say, you only fall the first million times!

L