That's a tough situation.
I think I would approach it by talking to your Boss about what makes you a more productive employee. Being healthy and having a balanced life will keep you from burning out on the job and eventually leaving.
If you are a good employee who your boss values... then he/she would want to you to keep working hard... but not burn out and leave.
You don't have to say... I MUST CYCLE... instead... just say that to stay sane and productive, you need to have some time for physical activity. And you are more than willing to put in the time, but there are some days when you might only work an 8 hour day, and you hope she/he can respect that... so you can keep working hard and not go nuts.
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"