  We present very low temperature scanning tunneling microscopy (STM)
experiments on single crystalline samples of the superconductor
$\beta$-Bi$_2$Pd. We find a single fully isotropic superconducting gap.
However, the magnetic field dependence of the intervortex density of states is
higher than the one expected in a single gap superconductor, and the hexagonal
vortex lattice is locked to the square atomic lattice. Such increase in the
intervortex density of states and vortex lattice locking have been found in
superconductors with multiple superconducting gaps and anisotropic Fermi
surfaces. We compare the upper critical field $H_{c2}(T)$ obtained in our
sample with previous measurements and explain available data within multiband
supercondutivity. We propose that $\beta$-Bi$_2$Pd is a single gap multiband
superconductor. We anticipate that single gap multiband superconductivity can
occur in other compounds with complex Fermi surfaces.
