I think this is related to (or the same question as:) How do I get to Beedle's island at night?, but the answers there don't really seem to answer the question.
Someone at the inn says that Beedle has a net I can buy, and that he's not there during the day.
I've tried going there at night, but I can't get to the bed (because it's under an outcropping, and my bird won't go in), and I can't see him out around during the day.
So, do I need to try harder to get to the bed on his island? Do I need to (wait until X occurs and) find him during the day?