I have years of experience with solar, and there is NO WAY I would put a non-glazed (open) collector on a tub. Doing so will run the tub into the range of 80 to 90 degrees (F) so you will have to kick in the heater to bring it the rest of the way. Personally, I want my tub hot (102F) at all times, so I don't know if there would be any real savings - I would first have to run a much bigger pump to move the water to the roof and back, and then add some heat during long chilly spells. We don't get "cold spells" this close to the ocean, so note that I said "chilly."
Glazed panels are pricey, and need to be cleaned regularly. They work great, but by time you pay for the cost of the extra pump, you may not have a net savings.
I know - HotSpring tubs ARE knows for energy efficiency, so maybe others will benefit from solar. I have put several on wood tubs - glazed and open. The glazed units can keep the tub at 102 all the time, the open units just keep it nice and warm, and a gas heater runs it up the last ten degrees or so.