I am trying to hook up a double switch (2 separate switches in the same box) (ceiling fan-light) in my bathroom
Each wiring group from the wall has 2 blacks 2 whites and 2 grounds

I have the light working by connecting the 2 blacks (1 per side of switch 2 screws) and wire nutting the two whites together and the same for the fan

The light comes on but not the fan

Should I connect one of the 2 blacks that work for the light to the fan switch since I know they work?

each wiring group from the wall has 2 blacks 2 whites and 2 grounds

Don't understand.

A wire is a wire, a cable is two or more wires in an outer covering.

By group do you mean cable and if so, do you mean that you have two cables with a black and white wire in each cable?