Not a broken bone, but I tore my right rotator cuff in a mountain biking accident a few years ago, and had to have surgery to repair that. I was in a sling with my arm mostly immobilized for about six weeks, and had several months after that where I was extremely limited in what I could do with my arm. Plus I had to go to physical therapy a couple of times a week. So probably not an altogether different experience mentally.

Advice? Hmm... tough to say. I hated not being able to ride during my recovery period, but I didn't really do anything special to cope. But I've always had something of a stoic approach to things (going back to before Stoicism was a fad among the tech bro crowd, mind you). Anyway, though it might sound trite/cliched today, I guess I would recommend reading some of the works of the Stoics and consider their mindset. Or some Zen Buddhist material might also be beneficial to you. I'm not a Buddhist, but I find a lot of value in the Zen mindset at times.

Otherwise, just fill your time reading, listening to music, watching movies, whatever you enjoy, and keep reminding yourself that you will be back to normal before you know it.