I live in Moscow. I have no job, but I do have a business visa and a bank account. That I managed to wire money into from Party. They changed the rules, though - they will now only wire money to banks in the country where you have your address listed. I have used other means to cash out so I didn't bother trying to prove residency, because I have like no bills or stuff that are actually in my name. It should be possible though - but do let them know in advance. I use Alfa Bank.
Another thing - do NOT get the homestay visa. AFAIK it will be a pain in the ass for your girl to make the invitation, involving multiple visits to a place with long lines. I use a business visa, and last time I checked I could stay 6 months at a time max. I got it through
www.rusvisa.org - they arrange for the invitation needed for the visa. It cost me 150 bucks for a 12-month invitation (the visa will still cost you extra - not sure about current rates, depends on your embassy and how soon you order in advance, too lazy to look it up right now).
For more qualified responses, I recommend
www.expat.ru (the forums).