There are about 7 Barrow Upon Humber records for the name of Bell from 1775 to about 1812 where the fathers name is recorded as Joseph, but only the 1 where the mothers name is Ann, that of your Joseph on the 3rd October 1808.
I suppose it is possible that Joesph Senior was a widower when he married Ann and thy only had the 1 child, that of your Joseph.
Barrow records on IGI do seem to be fairly comprehensive so it looks as if quite alot of work has been put into extracting the information.
Alan