For me, cycling is big part of quality of life and it impacts in where I choose to live and work. From what you described, sounds like being able to bike to work is very important to you, or otherwise it would not be such a struggle for you to make a decision. Again, personally, I would not change to a job which takes that option away from me. I tried to commute to work every day, and I can tell you on the days I have to drive (for whatever reason), I am definitely feel different in a negative way.
I would take the new job only if moving is part of the consideration.