I personally believe that exercise in any form is beneficial for body and mind and I think research has proved that exrercise is crucial.
A stationary bike may be a good start for you but getting out for brisk walks and possible a Pilates or dance class is also really good.
Don't try to go at things too much straight off - build up gradually and make the exercise part of your daily routine.
If you don't already do relaxation techniques, then do learn this, as exercise alongside some good relaxation can be great. DG x