Liquids with gas bubbles are commonly seen in medical science, natural science, daily life and engineering. Nonlinear-wave symbolic computation on the (3 + 1)-dimensional variable-coefficient Kudryashov-Sinelshchikov model for a bubbly liquid is hereby performed. An auto-Backlund transformation and with some solitonic solutions are obtained. With respect to the density fluctuation of the bubble-liquid mixture, both the auto-Backlund transformation and solitonic solutions depend on the bubble liquid-viscosity, transverse-perturbation, bubble-liquid-nonlinearity and bubble-liquid dispersion coefficient functions. We note that some shock waves given by our solutions have been observed by the gas-bubble/liquid-mixture experiments. Effects on a bubbly liquid with respect to the bubble-liquid-viscosity, transverse-perturbation, bubble-liquidnonlinearity and bubble-liquid-dispersion coefficient functions might be detected by the future gas-bubble/liquid-mixture experiments.