Secular evolution is one of the key routes through which galaxies evolve along the Hubble sequence. Not only does the disc undergo morphological and kinematic changes, but a pre-existing classical bulge may also be dynamically changed by the secular processes driven primarily by the bar. We study the influence of a growing bar on the dynamical evolution of a low-mass classical bulge that might be present in galaxies like the Milky Way. Using self-consistent high-resolution N-body simulations, we study how an initially isotropic non-rotating small classical bulge absorbs angular momentum emitted by the bar. The basic mechanism of this angular momentum exchange is through resonances and a considerable fraction of the angular momentum is channelled through Lagrange point (−1:1) and inner Lindblad resonance (ILR) (2:1) orbits. In the phase of rapid dynamical growth, retrograde non-resonant orbits also absorb significant angular momentum. As a result of this angular momentum gain, the initially non-rotating classical bulge transforms into a fast rotating, radially anisotropic and triaxial object, embedded in the similarly fast rotating boxy bulge formed from the disc. Towards the end of the evolution, the classical bulge develops cylindrical rotation. By that time, its inner regions host a ‘classical bulge–bar’ whose distinct kinematics could serve as direct observational evidence for the secular evolution in the galaxy. Implications of these results are discussed in brief.