We studied the swimming of Escherichia coli bacteria in the vicinity of the critical point in a solution of the nonionic surfactant C_{12}E_{5} in buffer solution. In phase-contrast microscopy, each swimming cell produces a transient trail behind itself lasting several seconds. Comparing quantitative image analysis with simulations show that these trails are due to local phase reorganization triggered by differential adsorption. This contrasts with similar trails seen in bacteria swimming in liquid crystals, which are due to shear effects. We show how our trails are controlled, and use them to probe the structure and dynamics of critical fluctuations in the fluid medium.