Call the manager for apartment. Ask for advice or help. If its raining outside or similar weather, humidity will be elevated. Think when it rains, 100% humidity. How long after you moved in did the symptoms of what you described become visible? Was it like that when you moved in?
Also, do a little homework and select good (try soft scrub type only- no abrasives) tub and tile type cleaner. There are many such as zep tub & tile cleaner and non-abrasive barkeepers friend, both very good. Mix together if you want to get benefit of both of there active ingrediets, glycolic and oxalic acids, which is what's reqired to dissolve scale, soap scum and dander build up. They are mild acids. Forget the bleach.. you are wasting effort, money & time. Also, forget about thinking the problem is coming up from down the overflow. That's nonsense. Problem is likely lack of normal, appropriate, frequent enough cleaning AND good chance you either aren't using the exhaust fan as often or long as you should each time shower utilized and/or the exhaust fan isn't evacuating the moist air at the minimal cfm rate per size of the bathroom. Many other variables, but these are you're most likely solutions.
If your manager allows you to remove cover plate or spray unknown drain line cleaner, that's between them and you. Hope the above proven remedies and ideas give you boost in right direction. Never hurts to do a lot of reading to get informed before acting. Highly unlikely your problem is the little bit of mold.. the problem is what gives rise to the presence of mold. In most cases its lack of proper cleaning, unless it's the exhaust fan not being utilized or not working properly in conjunction with not attending to the cleaning.
