Presuming if you have to leave for a job then you've got to get dressed and made up as well? I really can't think of anything that would explain that apart from "booty call". And then your mate might be like "chicks before dicks, girl".
I think either work, or chill with your mate, but not both. If you really need the cash then tell your mate you don't feel up to it. If you don't need the cash then tell the agency you can't work.