'Bachelorette' Andi Dorfman -- I'm a Lawyer ... Not a TV Fame Whore!

Andi Dorfman is NOT jettisoning her legal career for Hollywood ... so she claims in a private, plea to her D.A. boss.

The Fulton County D.A. made news a few days ago when he said the new Bachelorette resigned, after her leave of absence as an Assistant District Attorney expired. She originally took the leave to shoot the show, but after the resignation was announced everyone assumed she was giving up law.

Not so. TMZ got hold of her resignation letter, in which she says her TV obligations will wrap by the end of the year. And then she begs the D.A. to "strongly consider me for re-hire."

Andi says ... "my true passion is in the prosecution of criminal cases."

The D.A.'s office previously told TMZ they'd be open to bringing Andi back.