Why does it take a week for sand flea bites to show up?

Delayed reaction. Some people have delayed hypersensitivity reactions to the bite. Most of us are familiar with an immediate reaction - for instance a mosquito bites you and you immediately get a red, itchy bump. A similar reaction can be through a different pathway in your body, that can take days to activate and develop a reaction - it's called delayed hypersensitivity reaction, and likely what you are noting.