Recovery after a bone marrow transplant is gradual but most patients can walk throughout the transplant period barring a few days time when they have low blood counts. It could take several weeks for the new bone marrow cells which were infused into the blood to travel to the bone marrow to begin to make healthy new cells.  In some, it could take longer. This is why doctors will keep a steady watch on the recipients to monitor their progress.
Depending on the type of transplant, and the risks of complications, doctors could recommend light forms of exercising like walking for short periods within the transplant unit itself.