Previous studies have demonstrated that language switching in bilinguals can be affected by a number of variables, including the processing context. Here, we used a modified language-switching task combined with a Stroop paradigm, which manipulated the context of the task, to examine the impact of processing context on switch costs. The results of both Experiment 1 and Experiment 2 showed that the switch costs and the level of asymmetry in the switch costs are larger in the conflicting context than in the non-conflicting context, suggesting that the processing context affects the switch costs. In addition, the results of Experiment 2 revealed that individual variances in cognitive control capacity also play a role in the overall magnitude of the switch costs. Critically, processing context effects can be modulated by individual variance in cognitive control capacities. The results of this study are discussed within the framework of classic models of bilingual language control (e.g., the inhibitory control model).