We have used the galaxy modelling algorithm GRAVPOT16, to explore the most probable orbital elements of a sample of 64 selected N-rich stars across the Milky Way. We use the newly measured proper motions from Gaia Data Release 2 with existing line-of-sight velocities from the second generation of the Apache Point Observatory Galactic Evolution Experiment (APOGEE-2) and spectrophotometric distance estimations from STARHORSE. We adopted a set of high-resolution particle simulations evolved in the same steady-state Galactic potential model with a bar, in order to identify the groups of N-rich stars that have a high probability of belonging to the bulge/bar, disc and stellar halo component. We find that the vast majority of the N-rich stars show typically maximum height from the Galactic plane below 3kpc, and develop eccentric orbits (e>0.5), which means that these stars appear to have bulge/bar-like and/or halo-like orbits. We also show that ~66 per cent of the selected N-rich stars currently reside in the inner Galaxy inside the corotation radius, whilst ~14 per cent are in halo-like orbits. Among the N-rich stars in the inner Galaxy, ~27 per cent share orbital properties in the boundary between bulge/bar and disc, depending on the bar pattern speeds. Our dynamical analysis also indicates that some of the N-rich stars are likely to be halo interlopers, which suggests that halo contamination is not insignificant within the bulge area.