How much time should I spend in bed if I just had a hip reconstruction?

Not much. Patients who are more active are less likely to have wound healing problems, blood clots, or stiffness after surgery. Following surgery you should get the recommended 8 hours a night of sleep at night, but the rest of the time you should be up in a chair or walking about with assistance on a walker.
None. Assuming that you mean an uncomplicated total hip replacement, you should be up with physical therapy by the day after surgery if not the day of surgery.