My first reaction was "Are you nuts????" O.k., now my reasons. 1) If they have control of your bank account, you can be blamed for any financial misbehavior on their part and 2) it will be difficult for you to operate a company without access to the company's funds as needed. There is no reason that they could not be given copies of the bank statements at the end of the month but I would ABSOLUTELY NOT give them access to the bank account, itself.
You should be able to have legal agreements drawn up protecting their investment without potentially damaging YOUR credit and/or reputation.
The Virtual Office Goddess, LLC
I have to agree with office goddess. How can you possibly run a business if you don't have access to your funds? If it is an issue were someone else funded your business then you can create a contract and incorporate a silent partner. My advice to you is to consult your accountant and attorney to figure out the best way to keep both you and the investor happy without stepping on each others business toes.
I am planning to startup a business and due to various reasons, the investors would like to know, if they can retain full control of operating the Bank Account related to the company.
Ie, If I am the director of ABC Inc (or LLC) with just me working in it presently, and ABC has a bank account, can the sole operating person of the bank account be a complete outsider unrelated to the company?