Wow, I love reading your post! I intend to do this with my son as well. Right now, he's only two years old but when he's old enough to ride a bike, I want to ride a bike with him and my husband. We cannot find those attachment seats for bike from where we are which I'm quite bummed about. We tried putting a side attachment to the bike but my son won't stay put long. He wants to pedal as well like me, lol.
So we figured, we would just wait until he can ride his own bike. Right now, he has his little bike but cannot still reach the pedals. He uses this other car, and slides his feet in the floor to move it. Haha. We just wish he is that willing to pedal a bike when he's older. He doesn't even like the car we bought him which is automatic by the way, he prefers the manual car. Lol!