What are the chances of an air bubble during an epidural and how does this affect the procedure?

Low. The chances are low. The catheter is small and any air bubble would be tiny. If it does occur it would not cause a problem. It is not like having air injected into the blood suply.
No effect. The procedure for entering the epidural space is as follows. A needle is inserted into the space between the spinous processes (the bumps of bone on your spine). A syringe is attached to that needle. The needle is advance until a loss of resistance is felt in the syringe. That can be done with either air or liquid. Air will not cause any harm when injected into the epidural space.
? During epidural placement a small air bubble is placed in the syringe to help guide the needle to the right place. This is the standard procedure and the bubble itself casues no problems.