Firstly, から sounds a little strong for that context, it's usually reserved for requests to leave and such (Get out of my room ! ). The standard usage is を、部屋を出た and you don't need 私 or to repeat 部屋, unless there's some reason you do ?
It sounds grammatically perfectly OK to me, ので might be softer or less objective-sounding than から、or きちんとできる better than 片付ける, but those are personal judgments.
Of course you could also express it as 彼女が部屋を出て、 片付けられた。(つ is a づ）
which also indicates a cause without being so assertive or direct in the process. I'm thinking too that 'ga' may be more correct here....anyone ?
Unless she was obviously at fault for not leaving earlier or the speaker is actually trying to escape blame for not cleaning up after themselves, then 'kara' is good.
The awkward part of the sentence is は:
彼女がへやから出たから、へやをかたづけられる。
I think "katazukeru" is OK because it simply means "tidy up."
"(Kichinto) seirisuru" suggests that speaker has something specific in mind that s/he wants to rearrange in an orderly fashion. If that is what the speaker is thinking of, this one's OK, too.
"Deta" is correct. "Dashita" suggests there is someone or something that made her leave the room.