Nearly Headless Nick removes his head, tilting it politely in response. He doesn't know she is a Muggle. It is how he would greet any of the students here.

Hermione nods, as Crookshanks makes his way up to her. Laying down, so she can access the pouch at his side. "Yes. There is a ward around Hogwarts right now, to keep all the students safe. I couldn't leave to get these supplies."