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We report the single-crystal study of the bulk magnetization and neutron-scattering measurements on a quantum $S=1/2$ spin ladders system $\text{IPA-Cu}{({\text{Cl}}_{0.95}{\text{Br}}_{0.05})}_{3}$ with quenched disorder. In zero field, the disordered spin liquid phase is preserved as in pure ${\text{IPA-CuCl}}_{3}$. Due to the bond randomness, a different Bose glass phase was directly observed …