In reply to Dr Caterpillar:
When we were out there a couple of years ago a bus from the airport connected with incoming flights in Harstad and (I think) it was about an hours transfer to Narvik. We had relied on meeting friends at the airport (who missed their connecting flight) so hadn't done our homework on transfers but we had no problems asking for advice - the bus driver even gave us (clear) directions to our accommodation after dropping us off.
I would recommend Spor1 if you need basic affordable accommodation in Narvik itsself. Cheap (for Norway), clean and a choice of dorms or private rooms.