Disclaimer: I am not German, so I am basing this answer on the apparent equivalent of this word in Dutch: blijven. Usually this is safe, but very occasionally there is a mismatch between these two languages, so be wary.
I think it's probably not "staying somewhere" in the first sense you mentioned (Dutch: verblijven; separate verb). Waiting for someone and thus staying there could work, I think. Generally remaining in a place, or probably in a state, would work with "bleiben".
Will need to have a confirmation (or otherwise) from a native speaker though!