OK if I'm a new neighbor and they bring me a basket, I'd thank them right there and then without any further formal invitations.
If I bring the basket to them I would not expect an invitation to anything since I made the gesture without expecting anything in return.
However , next time I see the same neighbors I would try to start a conversation and get to know them better , without the pressure of a formal dinner invitation.
That's just me but I'm not from this country so I guess it depends on the culture, I'm guessing you'll get plenty of other recommendations so I'm curious to see what others think.