Robots of various forms have fascinated the public for centuries. Developments in micro- and nanotechnology are enabling smaller machines to be built, opening up new possibilities for applications. The use of microrobots for targetted drug delivery and minimally invasive surgery, for example, has received much attention. To understand one possible propulsion mechanism for microrobots, we model the swimming of flagellated bacteria. We use the boundary element method to solve the equations of fluid flow around the cell body and rotating flagellum and examine the trajectories of these swimmers in unbounded fluid, near flat surfaces, and colliding with suspended particles. Modelling the bacterial hook, which connects the flagellum to the body, as a Kirchhoff rod, we demonstrate that effective swimming is only achieved in a small range of values for the ratio of hook stiffness to motor torque. This suggests that the hook structure needs to be tightly regulated, as it is in bacteria. Our computations reveal that subtle differences in cell or flagellum shape can qualitatively affect the observed trajectories near surfaces. Taking these effects into account, we discuss how the motion of bacteria in microfluidic devices can be controlled by the design of the channels and how the motion of bacterium-like microrobots can be by controlled.