Greetings wisgaragedoor welcome to the Forum.
Every Shower/Sink/Tub/Commode "should" have what is called a "P-Trap", between where you access the facility, and the Sewer Line.
I wold presume that one was installed on your Shower, and via some unusual circumstances..
1. Separation in the Pipe.
2. Crack in the Pipe.
3. Improper Venting of that Line.
that the level of water in the Trap is being evaporated or in some other way, reduced to the point where the Sewer Gas is retuning into your bathroom.
You could get the Apt Mgr to hire a Plumber to do an investigation and repair, which you probably could "force" to happen, since those gasses are dangerous.
In the mean time, why don't you buy one of those flat rubber Sink Stoppers, and just lay it over the Shower Drain overnight/when not using the Shower, and start a serous* complaint process.
Have a good Day !
S.W.
* = Serious, like in a Public Health Issue.