D.P.
IMO, as long as she knows there is a "chance" you will come in--the hysterics will not stop.
Make a picture list of the routine: reads (book picture), brushes teeth (toothbrush picture), gets her a drink (picture of a cup), song (musical note), SLEEP (sleeping child).
Review the list with her during the day. Consult (with her) the list at night as you do the routine.
Is she in a crib? Leave her a sippy of water in the crib--or near the bed and put some soft music on 'repeat' on a CD player in her room.
Then THAT's IT.
You're not being mean, you know her needs are met, you're teaching her a skill she will need her entire life! Sometimes, the parent just has to grasp for sanity! Good luck!