The fastest way from northern Denmark to Bodø is to take the Frederikshavn – Oslo ferry then day train Oslo-Trondheim, then night train Trondheim-Bodø.
In general the Frederikshavn-Oslo ferry is a pretty good deal. It’s overnight (leaves Frederikshavn at around midnight and arrives in Oslo in the morning) but they don’t make you to book a cabin. They have recliner seats but apparently it’s ok to bring your air mattress and sleeping bag and just go in some corner. I can recommend the luggage room (more comfy than you’d think).
Only problem: At the moment the train service between Oslo and Trondheim is disrupted because of that collapsed railway bridge. There are regional trains that go all the way from Oslo to Trondheim via a more eastern route (Rørosbanen) but it’ll take very long and you’d still have to take the other train Trondheim-Bodø.

Cheers,
Felix