I know someone who ruptured his bicep tendon, and the doc said he could have surgery with a long recovery and normal appearance, or he could do nothing and it would look a little odd but the function and strength shouldn't be a problem.
He decided to do nothing and the doc was right....strength and function were not a problem....but you can definitely tell there is a moderate difference in appearance.
I will say this.....if you go ahead with the surgery, do it sooner rather than later. The more time that passes, the more painful it will be, as the tendon will ball up and contract, and it makes the surgery more painful. I experienced that during a quad tendon rupture....they kept me in the hospital for 4 days just to administer pain management meds....and there wasn't enough morphine in the world to make the pain go away. I was moaning in the bed and *the guy in the bed next to me (shared room)* actually told the nurses they needed to dope me up more. Not trying to scare you, just trying to give info. Granted, the quad tendon is much bigger than a biceps tendon, so pain should be much less. But good advice in here, listen to your doc and physical therapist and don't try to do things too soon.