Don't do any of the above, first establish if the alternator is ok or not.
With engine running touch a LIVE feed onto the "IND" terminal on the back, the terminal to which the blue wire goes, whilst watching a metre and if you see charging then start the alternator is ok, if not the alternator is duff.
Another check even simpler is too see if the IND terminal is EARTH without engine running, it should be, if no earth is present the alternator is duff.
If all checks out check live and earth at bulb holder as one will be missing, unless another blown bulb.
tabetha