The sentence is wrong in any case. "Bedroom" is not only a single word, but a countable noun - so it needs to be pluralised.
I am living in an apartment with three bedrooms.
However perhaps you meant to use it as an adjective? In which case the article applies to the apartment:
I am living in a three-bedroom apartment.
Most singular count nouns require a determiner, so the original sentence is correct. Your version (". . . a need for rebound") could work if "rebound" were considered a mass noun. I think that most people would consider that to be pretty unusual, though. ("Rebound" is normally a count noun.)