A: You may have bought a bum bulb that burnt out after a moment

B: The switch on the door that turns the light on and off could be bad.

Screw in a different bulb. Test your new bulb in a different socket. Push the fridge door switch by hand and release it several times to see if it comes on, even momentarily. A bulb of lower wattage should not blow a fuse, unless said bulb was defective in such a way that it shorted the connection. Any HF switching shouldn’t be an issue either, as it would be just turning the power on and off rapidly, and should be “seen” by any electronics in circuit as average power draw.