The worst “invite” is “oh, you’re always invited, call anytime”, b/c that is an empty invitation!
This assertion couldn’t be more inaccurate. …. In the days I was single, I had such people, and I would call them say on a Wednesday, asking “How are you doing”, and almost invariably they would ask, “What are you doing this Shabbos? Could we have you this Shabbos”, and given that a host[ess] can have several or zero guest on any one Shabbos, but the single person can only take up 1 invitation per Shabbos meal, this method is sincere & very productive.