I have a very bad smell coming from my shower drain - how can I get it to go away?

I would try Bleach. However, Your trap(Holds water,blocks sewer gas)
It may have evaporated because of not used, Run water for 20 seconds should easily fill trap.
Or Trap has leak. Water leaks out, gas in.

Most bad oders in bathroom drains come from rotting hair mixed with grease from the soap. Try this. Remove the two screws holding the strainer. (TIP; put the screws in the soap dish before they get lost down the drain.) Shine a light down there and with a bent coathanger fish out any hair that may be hiding down there. Then pour a 1/2 gal. of bleach down into the trap and let it set over night. Next morning flush the mess down with 2 latge pans of boiling water, (this is important). The bleach will desolve the hair and make it slippery and the boiling water will melt the grease and get the mess out of your drain. Smell better now? Cheers TOM