So when I start this bike, it runs fine in 1st gear, but when I shift to 2nd, & then 3rd it falls on it's face. After about 15 minutes of run time, it seems to run ok. Anybody have any ideas on what this might be?

I would check the carbuerator clean it out, check the air filter check float levels.JMO

Definatley do what melvin said, clean the carb.

Does it run better with the choke on?

I'd guess it's probably running lean. When an engine is cold it requires more fuel to run properly. Fuel is more likely to puddle when an engine is cold, once it warms up it will atomize much better and require less fuel because more will make it into the engine and not puddle in the intake track.

Take a piece of a wire brush (Realy small wire) and clean out the little holes in the main jet..

Sounds like a good project for this weekend. Thanks guys!

The good news, is my boy doesn't get out of 1st gear yet anyways. He's still a little scared of the throttle, but he's learning.

What bike did you get him?

It's just a little XR50. Got a good deal on it, so I had to pick it up.