How often should I contact my professor to "keep in touch"?

Hi, there is a former professor who I am close with, I believe, and I really do want to stay in touch with her. I’ve already graduated from this college and transferred to another school. She told me to “keep in touch and don’t be a stranger” when I graduated, but I wasn’t so sure how often I should visit or contact her through messengers. I visited her about 7 months after I graduated, and she told me again to keep in touch with her. I actually want to visit or talk to her more often, but I’m afraid that she might get annoyed or something if I contact her too often. How often do you think is appropriate for a student to visit or talk with a former professor?
Also, is it normal/appropriate for a student and a professor to have a lunch or dinner together in the U.S.? It’s totally common in my country, but I wasn’t sure about here.