<p>This paper presents a theoretical investigation into the dynamics of a transverse domain wall within a bilayer multiferroic heterostructure composed of a thick piezoelectric actuator and a thin magnetostrictive layer of hexagonal crystal symmetry. The study is based on the Landau-Lifshitz-Gilbert equation, accounting for the interplay of axial and transverse magnetic fields, spin-polarized electric currents, magnetoelastic effects, crystal symmetry, and piezo-induced strains. Explicit analytical expressions for key parameters, including polar angle, domain wall width, velocity, and displacement, are derived using a trial function inspired by the Schryer and Walker approach and employing the small-angle approximation. The results reveal that transverse magnetic fields, crystal symmetry, and piezo-induced strain are instrumental in modulating domain wall dynamics in the steady-state propagation regime. To be precise, the domain wall width directly depends on the transverse magnetic field strength, while the velocity is significantly enhanced under field-driven conditions, though it remains largely unaffected in current-driven motion. We emphasize that our findings align qualitatively well with recent theoretical and experimental observations, offering insights into tuning the dynamics of magnetic domain walls in multiferroic heterostructures.</p>