Sarah Brown, 23, is believed to have been at the Jolly Sailor pub on Poole Quay in Dorset at 9.30pm on Thursday.
Miss Brown posted on Facebook that her date had not turned up and she was having a drink with a man called Steve instead.
She was reported missing yesterday morning after failing to attend work on Friday or yesterday.
Force Incident Commander Ben Hargreaves, of Dorset Police, urged "Steve" to come forward to police.
"Sarah's family, friends and work colleagues are becoming increasingly worried because her disappearance is completely out of character," he said.
"Concern is also increasing as it is possible that Sarah may be upset due to the approaching anniversary of a family tragedy.
"I ask anyone who knows the whereabouts of Sarah, or Sarah herself, to make contact with someone as soon as possible - we just need to know that she is safe and well.
"I urge the man she met called Steve to come forward - you may have information that can assist in locating Sarah.
"Anyone with information should contact the police urgently on 101."
Miss Brown, of Ashley Road, Poole, is described as white, 5ft tall, of medium build with long black hair.
She was last seen wearing black skinny jeans and a purple blouse.