I can share my experience with you. My family moved up to Beijing in 2006 for a year. Not sure now, but at that time I let my maid applied the Chinese travelling visa. It depends on how long they liked to give. Sometimes one month or luckily three months.
Then, once we moved up there, look for those local agents which specially in applying working visa for foreigners. They will find a way to get a working visa for your miad. But of course not in a name of maid visa. China will not allowed any maid working visa. You may be surprised to know that your maid is a manager in a whatever company.
I did not ask in detail how the agent did it for me. As long as my maid could officially stay and worked for me.
Hope it can give you some idea.