I think you can solve this problem without storing any bank information yourself through using something like Paypal’s Mass Payment API. That way, your client can pay people, and PayPal stores all the information so you don’t have to.
If you want to read about all of the steps you need to take to even have a remote possiblity of securing your client’s sensitive financial data, google ‘PCI Compliance’
If you’re not deathly afraid of storing financial data online, you’re horribly naive.