This reminds me of an evening commute last year where I rode into a bmx vs road bike race. I already had 14 miles under my tires at the point where I rang my bell to indicate that I wanted to pass a group of teenage bmx riders noodling around the MUP. One decided to take off sprinting. I caught up in less than 10 seconds and blew by him. Granted, I wasn't starting from standstill, but I don't think a bmx has a chance once its speed tops out.

Edit to add: I think I probably caught up in about 5 seconds, and I didn't get out of the saddle to sprint either, just spun up to pass him nonchalantly.