To successfully perform biological experiments on bacteria in microfluidic devices, control of micron-scale cell motion in the chip-sized environment is essential. Here we describe a new method for simulating the motion of individual bacterial cells in a microfluidic device using a one-way coupling Lagrangian approach combined with rigid body theory. The cell was assumed to be an elastic, solid ellipsoid, and interactions with solid wall boundaries were considered to occur in one of two collision modes, either a "standing" or "lying" collision mode on the surface. The ordinary differential equations were solved along the cell trajectory for the thirteen unknown variables of the translational cell velocity, cell location vector, rotational angular velocity, and four Euler parameters, using the Rosenbrock method based on an adaptive time-stepping technique. As selected applications, we show how this novel simulation method may be applied to the designs of efficient hydrodynamic cell traps in a microfluidic device for bacterial applications and for cell separations. Modeled designs include optimized U-shaped sieve arrays with a single aperture for the hydrodynamic cell trapping, and three kinds of staggered micropillars for cell separations.