And my imagination kept me unconcertrated for the rest of the lesson. Jeg er så alene.
Is there any way how to differentiate between bath and bathroom in a context-free way?
I don't think so. And it can also mean swimming pool. I've gotten them muddled up a few times with context, let alone without. Sometimes people use 'baderom' for bathroom. Also, it's common to use toilet (do, WC, toalett).