It's not from being bitten, it's from the cat swallowing the flea when they clean themselves.
From the Centers for Disease Control website:
"By swallowing a flea infected with a tapeworm larvae. A dog or cat may swallow a flea while self-grooming. Once the flea is digested inside the dog or cat, the larval tapeworm is free to develop into an adult tapeworm.
The adult tapeworm is made up of many small segments, called proglottids (pro-GLOT-ids), each about the size of a grain of rice; adult tapeworms may measure 4-28 inches in length. As the tapeworm matures inside the intestines, these segments (proglottids) break off and pass into the stool."
I don't remember the time frame exactly, but I think it can be up to 6 months later. Hopefully someone will be along with a more precise answer for you on the time.