Head off

In a bar:

Frank pays the bartender. Then gives Anna a hug and heads off. Anna takes a sip of her beer, then notices that he's forgotten his cap. She turns to look for him, but he's left.

Is 'heads off' OK here if Frank is heading for the door to leave, but we don't see him leaving the bar? Or do you prefer something else? Maybe 'heads for the exit'? Thanks.