I think what the OP is asking for is for the PDF invoice to be attached to the email which Dreamhost sends him. But doing that might be considered bad business practice for a number of reasons.
Actually, if you have Dreamhost in your browser's bookmarks and are willing to have your browser's password manager remember your password, it is only five clicks to download the invoice.
- click on Dreamhost bookmark
- form is pre-populated, click on 'sign in'
- click on 'manage account' in 'quick links'
- click on 'what are these charges?'
- click on 'download PDF invoice'
It took less than 20 seconds from a standing start, and that is using a geostationary satellite and a laptop pointing device. I think that someone with a proper mouse and a terrestrial internet link could do it in 5 seconds.
But if anyone can locate a host where one can download the latest invoice in four clicks or fewer, I will consider moving to them.