I think if you ask for a contract with property manager, they will shy away from you. I agree with Jeremy, quote your prices, promise prompt and quality work, and maybe ask to do one free of charge to show what a great job you’ll do.
When I first started, one of the things that got me in was a promise of same day service but couldn’t promise a specific time in those instances. They appreciated that and usually gave me a try. Once they find out you do great work, they will be willing to wait if they need to.