Use existing light switch to also power bathroom exhaust fan?
You can use the switch to operate both the fan and light, if you so choose.  In fact, this is a common feature in single user public restrooms.   As long as the switch and wiring are rated for the amount of current, which unless you get a huge fan, it should be.

If you have the ability to install a new cable (or pull an extra wire, if the wires happen to be in conduit), you could use a device that has two switches that fit in a single gang box.  Which would allow you to control each device separately.