Usually caused by inductance from nearby active wiring ,it doesn’t take a lot of power to charge up the capacitors in a CFL.
Does the bathroom have dual switching for the light i.e two separate on/off switches? (or an illuminated switch?)
Getting static from somewhere. Remember if you have enough static on your body, you can light-up fluorescent bulbs by holding it. Stick small square of Aluminum foils close to bulb socket on base might help.
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Light socket wired backwards???
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I dont have a clue what might be happening in your case Phil other than it possibly being a landing beacon for visitors from the 8th dimension. Pop an led in there and see what happens
But on a related note, I have been swapping out my bulbs for led’s and in cieling fan fixture in the living room, one that has a pull chain as well as a 3 way switch setup (2 switches in different locations) if the pull chain is “on” and the switches are off, the bulb will faintly glow enough to be seen clearly in the dark.
I suspect a bit of current leaks past the 3 way switches and since the led only needs a gnat’s fart of current to fully illuminate a few millivolts will affect it as well?
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Perhaps the switch is on the neutral side of the socket and the hot is always connected to the bulb.
Do you have any voltage between your neutral and ground?
Weird.
Wild guess - do you live close to a radar installation?
With a 3 way switch current always passes through the individual switch to feed the other in the circuit an if there is a slight fault within (or not even) a minute bit of current can leak through.
In your situation, I am leaning toward the inductive capacitance theory…
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Dimmer switch in use?
GFI?
Stumped 
Replace with LED?
Seriously, any abnormality connected to house wiring needs to be investigated and resolved in a professional, timely manner IMHO.
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The length of unconnected mains wire to the bulb when the switch is off is acting as an antenna. Like a cats whisker radio circuit. The circuit in the bulb rectifies it charges up the small capacitor in the on board circuitry and the tube fires when the voltage gets high enough. Been there. Its very annoying but not dangerous. Try changing to a different brand of compact flourescent light bulb.
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The capacitors could be draining, pulsing the lamp.
Can’t help with the problem, but can share an amusing anecdote…
Friend of mine (who is an electrician) and his wife, kept being awoken at night by what appeared to be “camera flashes” in his bedroom.
Suspecting everything from the CIA, aliens and deviant neighbours, he spent weeks trying to find the problem.
Turned out, the lighting circuit for the down lights above their bed, was picking up an induced current from adjacent wiring in the house. This was charging up a capacitor somewhere in the downlight system in his bedroom (I know nothing about electricity, so my explanation may be wrong). When the current was sufficiently high, it would all discharge at once, creating the “flash”.
He says his wife still doesn’t believe him, which has had an effect, requiring no further explanation here.
If you have a loose neutral, a motor ( like your refrigerator) could be sending spikes. So check your neutrals in your panel.
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I believe this is a case of ghost voltage. Try running a ground (temporarily) from the fixture ground to true ground (if you have one), I bet it stops instantly.
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Yea, the power to run the switch light runs through the fixture. This charges the capacitor till its full then it try’s to light the lamp, but there’s not enough power so the lamp goes off. Starts all over again
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