Bathroom ceiling vent has a fan cover, and a duct behind it but no wiring. What does that do?
It is possible there is an "inline duct fan" half way along the duct. 



These are "designed to produce higher working pressures for applications that require high air flows, with low relative noise." compared to cheaper surface-mounted fans.

Your duct presumably runs through your attic/loft and is accessible from there.

There will probably be an isolation switch for the fan somewhere just outside the bathroom. This may incorporate a fuse. If so, you could check the fuse is Ok and that the switch is working.

Typically, power to the fan is provided via a pull-cord operated light-switch and often there is a separate permanent-live feed so the fan can continue to extract damp air for several minutes after the room has been vacated.