Money management

[private joker]

Here's my problem. My bank (Bank of America) has a limit to the amount you can withdraw from the ATM on any given day, as most of them do. It's $500. I have a more substantial amount of funds that I want access to daily, up to $800 or $1,000 at a time (reasons are immaterial, but let's just say it's so I can buy in at a 10/20 table somewhere).

How can I manage this? I'd rather not keep the money unsafely in my apartment, sitting in an envelope somewhere, but if I put it in BofA, I can only take out $500 at once. Other banks have told me they can sometimes increase the limit, but it's based on account standing, of which I have none at banks other than BofA.

Anybody?