We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial response and the adaptation to the sustained concentration of the chemical. This was carried out by tethering motile cells by their flagella to glass slides and following the rotational behaviour of their cell bodies in response to the nutrient change. Computerised motion analysis was used to analyse the behaviour. Distributions of run and stop times were obtained from rotation data for tethered cells. Exponential and Weibull fits for these distributions, and variability in individual responses are discussed. In terms of parameters derived from the run and stop time distributions, we compare the responses to stepwise changes in the nutrient concentration and the long-term behaviour of 84 cells under 12 propionate concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for the random walk approximation to bacterial swimming and compare them with the observed R. sphaeroides motile behaviour.