Navigation of cells to the optimal environmental condition is critical for their survival and growth. Escherichia coli cells, for example, can detect various chemicals and move up or down those chemical gradients (i.e., chemotaxis). Using the same signaling machinery, they can also sense other external factors such as pH and temperature and navigate from both sides toward some intermediate levels of those stimuli. This mode of precision sensing is more sophisticated than the (unidirectional) chemotaxis strategy and requires distinctive molecular mechanisms to encode and track the preferred external conditions. To systematically study these different bacterial taxis behaviors, we develop a continuum model that incorporates microscopic signaling events in single cells into macroscopic population dynamics. A simple theoretical result is obtained for the steady state cell distribution in general. In particular, we find the cell distribution is controlled by the intracellular sensory dynamics as well as the dependence of the cells speed on external factors. The model is verified by available experimental data in various taxis behaviors (including bacterial chemotaxis, pH taxis, and thermotaxis), and it also leads to predictions that can be tested by future experiments. Our analysis help reveal the key conditions/mechanisms for bacterial precision-sensing behaviors and directly connects the cellular taxis performances with the underlying molecular parameters. It provides a unified framework to study bacterial navigation in complex environments with chemical and non-chemical stimuli. 