我推荐：
I wonder when it will be convenient to have your room cleaned?
客气，用I wonder最符合英语习惯，when it will be convenient也是英语里有的说法，即是否可以，是否方便的意思。 have your room cleaned,清理您的房间，也是符合英语习惯的。所以我觉得这样说既客气，又能明确表达您的意思。
My when facilitates cleans up your room
或
When do I facilitate clean up your room
what time I clean your room is covenient?
What's the best time for me to clean the room?
When it is convenient to me to clean your room?
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