Do you get mileage to drive to AIT when you are reclassifying or will the Army provide me a plane ticket?

It depends on how far the school is away from your duty station, if you're going in a TDY and return status or TDY enroute and if you're authorized to have a vehicle there or not. All stuff that can be found out through your DTS manager or the ATRRS catalog.

You'll go TDY enroute. The Army will give you a plane ticket. If you choose to drive you will only be reimbursed for the cost of the plane ticket. Plus, you may have to take some of that driving time as personal leave. The mileage you're paid for the TDY portion is at the mileage rate, while the follow on PCS portion is at the PCS rate.

You will be considered a MOS-T, so you will be authorized to have a vehicle and will not be housed with the new Soldiers that arrived from basic training. Once you are halfway through the course, you will receive new assignment instructions under your new MOS. If you want/need to be able to get around I highly recommend you to drive because you won’t have the same restrictions as the new Soldiers. I hope this helps, good luck to you.