Is it possible to store the credentials of a user so that they can just call us up and we can send them an invoice with any jobs they may have had over the course of the month?

All the past jobs are stored in the Dashboard and you can view a particular date range such as one month which is the default.
Something else we have done with stored credentials is giving customers a log in so that they can select and quickly re-book their previous jobs. This is useful if the same job is required on a regular basis. The exception to this is that we never store customers credit card details. For security and to comply with legal requirements, you should never store credit cards on your website.