Recent studies in heavily hole-doped iron-based superconductor RbFe$_2$As$_2$ have suggested the emergence of novel electronic nematicity directed along the Fe-As direction, 45$^\circ$ rotated from the usual nematicity ubiquitously found in BaFe$_2$As$_2$ and related materials. This motivates us to study the physical properties of Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$, details of which remain largely unexplored. Here we report on the normal-state charge transport in Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ superconductors by using high-quality single crystals in the range of Rb concentration $0.14\le x \le 1.00$. From the systematic measurements of the temperature dependence of electrical resistivity $\rho(T)$, we find a signature of a deviation from the Fermi liquid behavior around the optimal composition, which does not seem related to the antiferromagnetic quantum criticality but has a potential link to hidden nematic quantum criticality. In addition, electron correlations derived from the coefficient of $T^2$ resistivity show a marked increase with Rb content near the heavily hole-doped end, consistent with the putative Mott physics near the $3d^5$ electron configuration in iron-based superconductors.