Despite knowledge about microbial responses to abiotic stress, few studies have investigated stress responses to antagonistic species, such as competitors, predators and pathogens. While it is often assumed that interacting populations of bacteria and phage will coevolve resistance and exploitation strategies, an alternative is that individual bacteria tolerate or evade phage predation through inducible responses to phage presence. Using the microbial model Pseudomonas fluorescens SBW25 and its lytic DNA phage SBW25Φ2, we demonstrate the existence of an inducible response in the form of a transient increase in population growth rate, and found that the response was induced by phage binding. This response was accompanied by a decrease in bacterial cell size, which we propose to be an associated cost. We discuss these results in the context of bacterial ecology and phage-bacteria co-evolution.