Edinburgh-Bergen-Bodø:
fly Loganair and Widerøe, visit the beautiful city Bergen before heading north
London- Bergen- Bodø:
Fly Widerøe all the way, two flights
Copenhagen- Trondheim – Bodø:
Fly SAS and Widerøe, two flights
Hurtigruten from Bergen to Bodø, or Trondheim to Bodø, 60H/ 24h voyage.
Daytrain from Trondheim to Bodø (requires hotel in Bodø)12 h journey (could also be done as a night train, but that will destroy your sleep).