I know what you mean about the roaming cats. All my cats have always been indoor cats for that reason. I also don't want them getting run over, or have anything else bad happen to them.
Perhaps you need to work your way up to the BMX bike slowly. Perhaps riding a mountain bike, or a hybrid. Something that won't scare your mom.
I have to say though, I looked at the Long Island CL, and man, there's a lot of BMX bikes. We don't have nearly that many here on the Seattle CL. I did think this was interesting:
http://newyork.craigslist.org/lgi/bik/305705203.html
Mostly because $90 for two bikes in your area is almost criminally cheap, especially for the coupled bike.
East Hill