Second hand cars are not expensive here. Taking the bus is a bad idea, specially during rush hour. With the heat outside reaching the 40's and 50's waiting for a bus for 30 minutes is unhealthy and extremely uncomfortable. Taxi's are indeed a problem, they phased out all of the old taxis before providing enough replacements. Hopefully the problem will be sorted out by December, but it may not be.

Mowasalat, the company that runs the taxis, provides school transportation in the form of cars, and sometimes buses. It might be useful to call them and ask what kind of arrangement can be made for your son, even if it is temporary.

If you have a license for a car you have to take a 2 week refresher driving course, then a driving test. For some nationalities, such as Americans, their driver's licenses are automatically accepted and transferred to Qatari licenses. I dont know how to apply for a motorcycle license.

Bring the darn motorcycle, but as a back up. Hope your transportation problems get sorted out.