How old are you? Just curious? And yes you can be fired, or forced to take a drug test if your employer suspects you of drug use. The only way they wouldn't be able to is if you had a union or contract stating that you don't have to submit to testing unless just cause.
I'm willing to bet it's either you mentioning use to people, or the way you act. I can spot a guy new to gear a mile away, or just those guys who feel cool because they are using. Not to mention any gym owner with half a brain should be able to spot someone who uses, especially someone new to it.
How many times in you life do you all the sudden add 10-20lbs? There are thousands of guys here who have been doing this for years and there will always be those who think if you have any decent size that you are on something, but most have no issues because they keep it to themselves.
Maybe her concern is you strike her as the type to suggest or offer gear to clients in her gym. Unfortunately it's still illegal, yet you can stop at any corner store and buy bath salts then eat someones face, but that's a different story, point is she may not want her employees associated with anything illegal and apparently doesn't seem to trust your judgmental skills because it's also good for a gym to have trainers who look like they lift, but it seems that shes more concerned over how you will impact the business.
Sorry to sound negative man, and I'm not bashing you, but it sounds to me like you are giving off the "look at me I'm on gear vibe" or have been talking to people, or she has a brain and can see it, but doesn't trust you to keep it quiet. It's pretty common for employers to test if the have valid concern that an employee is using illegal substances.