Just get rid of your mailbox. IANAL, but I really doubt you’re legally required to maintain a mailbox, so just throw it away and they won’t be able to deliver your mail any more.
If your girlfriend still wants to receiver her mail, you might have to get rid of her, too. Or if you’d rather keep her around because you like her or whatever, get a PO Box.
Although I get a lot of junk mail at my residential mailbox, I get maybe two or three pieces of junk a month at my PO Box even though it’s published online and I use it almost exclusively. I bet that’s because the bulk mailers don’t target PO Boxes since almost everyone has a residential mailbox. Of course, the downside is that you (or your girlfriend) have to go to the Post Office to get your mail.