Anna's at work when she gets an invitation to a going-away party at a local bar. A girl she works with is leaving, and is popular enough that a huge shindig is necessary.
It also means she won't care if Anna brings a guest.
Elsa can't drink, but it's more about getting out of the house. Out of her own head. Sometimes she's just so quiet. Anna has work, but Elsa doesn't; she has no idea how her housemate spends her time.
Plus, it would be nice just to go out with her.