A lady I know who is baalas teshuva told me that before she became Frum, when she saw Frum people around (I guess her neighbors, etc.), she always wanted them to invite her family for Shabbos. When she saw them building their Sukkahs, she always wished they would invite her to come eat in the Sukkah. Often, we are too afraid of reaching out to not-Frum people because we are afraid of how it will be perceived, and meanwhile they are waiting for us to reach out to them.
Obviously, one must use one’s seichel and sensitivity in how they go about this. You have to be normal. But a Shabbos invitation extended sincerely is always in place.