What is the normal recovery time for biceps tenodesis surgery?

Depends. Thae answer depends on the method for fixing the biceps tendon. Usually, there are some sort of limitations for the first 6 weeks, although your surgeon will be able to be more specific depending on the details of your procedure.
Varies. Recover time will vary depending on many factors including age, general health of the patient, infection control, blood sugar control, the exact type of procedure, and post-operative and follow up care. Discuss it with your surgeon and get their opinion as to what they feel is a reasonable recovery time for you.