I have a electric baseboard heater in my bathroom which does not work.
I just bought this house, so no idea if it ever did. I opened up the
thermostat and checked to see if the thermostat received any power at
all. It seems there is no electricity flowing to the thermostat
connection and hence the electric baseboard. ( Iused a electric bulb
set to complete the circuit )

Since the wires are behind the wall, is there any way to check where
the fault might be? All other lights etc in the bathroom work fine.

I don't see that anything has tripped.

Thanks