I would guess it isn't some spy-novel restricted area, but simply some codes on doors to stop the general public from going where they shouldn't. I imagine the clinical waste was safe in a tub/bucket- type disposal unit, and would just be emptied in the cellar.
Interesting that everyone has assumed the guy was young, just because he is a trainee.
He is a fully functioning adult who CHOSE to stay where he was, rather than do as the OP advised and ring someone else.
This wasn't bullying - this was a nosey trainee wandering into areas he shouldn't be in. He then is given clear instructions as to how to get out, but chooses not to, because he knows he has already had a bollocking for doing similar earlier in the week ( and would probably jeopardise his job)
I am a bit
that people have called him "keen". Keen would have been hurrying down to dispose of the clinical waste and returning quickly as he had both been instructed to , AND more importantly said he was going to do.
If he had done so, they could both have continued on with their work/out of office meeting. As a manager, I would be pretty pissed off with someone who said they were going to do x and then saw it as an opportunity for a bit of a skive and a nosey around.
As it was, OP waited HALF AN HOUR for him, before leaving to continue with her job.
NONE of this is Op's fault. She could have handled it better, though.
She should have reported him earlier. She should have contacted him to check where he was ( in case of injury/sickness) + to say that she was leaving and to do xyz until her return.
I have low tolerance for people who wander off when there is work to be done.
If he had made a genuine mistake, he should have rung someone else to let him out and have been doing something constructive until OP got back. As it was, he didn't do that. That tells me that he was skiving and in an area that he wouldn't easily be able to explain away.
I don't think OP is a bully. I think she actually needs to learn to be more assertive - I certainly wouldn't be bullied into giving codes/agreeing to a skiving mission just before I was due to take a trainee to a meeting off site. The Trainee sounds like a waste of resources to me.