A few years ago I broke my fibula but also my tibia plateau. It wasn't the fibula my doctor was worried about, but the tibia plateau required surgery. The fibula healed on it's own (but it was also a break at about the mid-point of the leg). It's actually what got me into cycling because not only did I break the top of the tibia bone but also displaced the knee joint, thus raising my chances of arthritis in that knee. The doc recommended low/non-weight bearing exercises to recover and I chose the bike and haven't looked back since (thankfully there's been no real pain from the leg in the last year and a half).
My guess is once the leg is healed, or pretty close to it, you can ride without much pain. In fact for me I had to walk in crutches over to an exercise bike during my treatment and could ride for an hour without pain. I just couldn't walk on that leg yet. Funny how that works out.