What are the risks and the recovery period for a carotid subclavian bypass?

Safe procedure. This is generally a safe procedure in most patients. There are risks to injury to nerves, including nerves to the diaphragm, tongue, and voice box. There is a risk of injury to the thoracic duct, a major lymphatic vessel that can be close to the subclavian artery. Overall, these risks are low. Most people recover easily within 24 hours and go home the next day.
Surgery. There are risks with any surgery. Did you make your surgeon answer these questions before they decided on the procedure? If not, then you need to do this asap. If they don't answer to your satisfaction, then get a 2nd opinion!