Let's suppose I am flying at constant bearing (initial and final heading are equal and constant) relative to the geographical north pole; what kind of trajectory would I be flying?
The term bearing is not so clear, as the link to another answer in the comment shows.
But let's say bearing means the angle between the track (over ground) of an aircraft and a fixed location. This position usually is the magnetic or (true) geographic north, but within the context of this question, it could also be any location on earth.
If the bearing is 90° or 270° (perpendicular to fixed location), the aircraft just flies circles, in case of using the geographic north, it flies along a line of constant latitude.
If the aircraft is flying at a different angle, the trajectory is a spiral, more precisely a Rhumb line, with curls around that location and the location at the opposite side of the earth:
BUT due to the magnetic deviation, the magnetic field doesn't point to the (magnetic) north pole everywhere on earth.
I simulated the trajectory for a quite similar question here. The red arrows indicate where the needle of a compass points to. The black line is the trajectory for an aircraft flying a 90°-track with respect to the local magnetic field. It is just a deformed circle.
The blue line is the trajectory of an aircraft flying a 93.6°-track. This is a deformed Rhumb line, and the aircraft coming from KLAX will circle around the magnetic pole at some point like a moth around a light. (at least mathematically)