Context. The structure and kinematics of the old component of the Galactic bulge are still a matter of debate. It is clear that the bulk of the bulge as traced by red clump stars includes two main components, which are usually identified as the metal-rich and metal-poor components. They have different shapes, kinematics, mean metallicities, and alpha-element abundances. It is our current understanding that they are associated with a bar and a spheroid, respectively. On the other hand, RR Lyrae variables trace the oldest population of the bulge. While it would be natural to think that they follow the structure and kinematics of the metal-poor component, the data analysed in the literature show conflicting results. Aims. We aim to derive a rotation curve for bulge RR Lyrae stars in order to determine that the old component traced by these stars is distinct from the two main components observed in the Galactic bulge. Methods. This paper combines APOGEE-2S spectra with OGLE-IV light curves, near-infrared photometry, and proper motions from the VISTA Variables in the V & iacute;a L & aacute;ctea survey for 4193 RR Lyrae stars. Six-dimensional phase-space coordinates were used to calculate orbits within an updated Galactic potential and to isolate the stars. Results. The stars that stay confined within the bulge represent 57% of our sample. Our results show that bulge RR Lyrae variables rotate more slowly than metal-rich red clump stars and have a lower velocity dispersion. Their kinematics is compatible with them being the low-metallicity tail of the metal-poor component. We confirm that a rather large fraction of halo and thick disc RR Lyrae stars pass by the bulge within their orbits, increasing the velocity dispersion. A proper orbital analysis is therefore critical to isolate bona fide bulge variables. Finally, bulge RR Lyrae seem to trace a spheroidal component, although the current data do now allow us to reach a firm conclusion about the spatial distribution.