Could you host Emily? A room for 2 months

After leaving an abusive relationship, I'm temporarily without a home. I work as a line cook in Brooklyn 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 3 months. I can pay $340 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 two work 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. Thank you so much.