Do you see how he looks at her? Even dressed as a lunch lady he thought she was beautiful. I can imagine 1 of the students noticing this and discussing with their friends how they ship Mr. Smith and the new lunch lady.
My favourite picture of Rose with the TARDIS. The TARDIS loved Rose just as much as the Doctor did so it’s no wonder she opened up her heart so that Rose could save him. <--mind you, it did take a truck to convince her.