I think you might be looking for something that doesn’t exist. All the bingo rooms are going to want you to register before you play because then they can try to convert you into a real money customer.
You might like to try http://www.desperatehousewivesbingo.com – they meet your first two criteria at least. They’ve been doing very well for me over the last couple of months.
Affiliate program is here : World Bingo Affiliates