The use of B-spline basis sets is explored in the context of a vibrational program for automatic potential energy surface (PES) construction and multimode anharmonic vibrational wave function calculation. Results are compared with calculations using localized Gaussians and harmonic oscillator basis functions. Potential energy surfaces are constructed in an iterative fashion using a recently developed adaptive density-guided approach. The basis set requirements for an accurate representation of the vibrational wave functions are met by both B-spline basis sets as well as the well-known distributed Gaussian basis sets. Furthermore, the property of minimal support of the B-spline functions makes the use of B-spline basis more advantageous compared to harmonic oscillator basis functions, when combined with the adaptive procedure for PES construction used in this work. The methodology is tested for model potentials and water and subsequently applied to study vibrational states of dioxirane and diazirinone. The latter have proven to be elusive to experimental characterization and high level vibrational calculations based on accurate PES may offer a guidance for the experimental work.