I'm trying to find a solution or service that will allow for my company to automatically take a customer's credit card information via the web to keep on file and bill against based on how much they have used the services we provide. We need a service that will also handle the payment processing as well.

Note that this is not recurring billing. The bill at the end of each month won't be the same.

Presently, we are having to take a customer's credit card information over the phone and manually input it into Quickbooks, but this just doesn't work for scalability. We will still be manually invoicing the customers, but we need automated credit card acceptance and storage without the liabilities involved with storing it on our own server.

Solutions that integrate with Wordpress would be a plus.