A spare room for 4 months: Florin, working in București, between homes

After being laid off and unable to cover rent, I'm temporarily without a home. I work as a hospital cleaner in București and I have a steady income, but I can't find a place that will let me in without the first month, a deposit and references that I'm in the middle of replacing. I'm looking for a spare room for 4 months. I can pay $60 a month toward bills, I'm tidy and quiet, and I'd be happy to help with cooking, shopping or yard work. I have no pets, I don't smoke, and I have a landlord and employer references. I understand that inviting a stranger into your home is a big step. I'd be glad to meet in a public place first and to share my work details. Please ask me anything in the questions section. I'll answer honestly and quickly.