TMZ has obtained a letter that Melissa Smith -- Jesse James mistress #2 -- faxed to Sandra Bullock's agent on Sunday, apologizing for her alleged affair with Jesse ... and it's pretty audacious.
Smith wrote to Sandra, "I felt I needed to reach out to you and tell you how deeply sorry I am for everything that you've been through."
Smith goes on ... "And I know nothing I can say in this letter is going to make the pain of my actions go away."
And the mea culpa continues: "... I am sorry for any hurt or pain that I have caused you. My actions of engaging with a married man are unforgivable. I never meant you any harm."
Smith continues, "I compromised my beliefs on several occasions and as a result will never forgive myself."
Melissa closes the letter, "Please contact me if you wish to discuss on the phone or in person."
Don't wait by the phone, honey.