  We investigated the superconducting properties of the topological
superconductor $\alpha$--PdBi$_2$ at ambient and external pressures up to
1.77~GPa using muon spin rotation ($\mu$SR) experiments. The ambient pressure
measurements evince a fully gapped $s$-wave superconducting state in the bulk
of the specimen. AC magnetic susceptibility and $\mu$SR measurements manifest a
continuous suppression of $T_{\rm c}$ with increasing pressure. In parallel, we
observed a significant decrease of superfluid density by $\sim$20\% upon
application of external pressure. Remarkably, the superfluid density follows
linear relation with $T_{\rm c}$ which was found before in some unconventional
topological superconductors and hole doped cuprates. This finding signals a
possible crossover from BEC to BCS in $\alpha$--PdBi$_2$.
