Are you sure it was Bogart?
There are plenty of real-life stories of him actually being in a wheelchair when he was dying of cancer. He used to be carried downstairs by his staff to sit in a wheelchair to hold court among Hollywood's finest.
But could it be that you are thinking of James Stewart who was stuck in a wheelchair with nothing to do but spy on his neighbours in Hitchock's Rear Window?
If you have more detail - post an answer to this question and I'll go back on the trawl.