Bilingual speakers are suggested to use control processes to avoid linguistic interference from the unintended language. It is debated whether these bilingual language control (BLC) processes are an instantiation of the more domain-general executive control (EC) processes. Previous studies inconsistently report correlations between measures of linguistic and non-linguistic control in bilinguals. In the present study, we investigate the extent to which there is cross-talk between these two domains of control for two switch costs, namely the n-1 shift cost and the n-2 repetition cost. Also, we address an important problem, namely the reliability of the measures used to investigate cross-talk. If the reliability of a measure is low, then these measures are ill-suited to test cross-talk between domains through correlations. We asked participants to perform both a linguistic- and non-linguistic switching task at two sessions about a week apart. The results show a dissociation between the two types of switch costs. Regarding test–retest reliability, we found a stronger reliability for the n-1 shift cost compared to the n-2 repetition cost within both domains as measured by correlations across sessions. This suggests the n-1 shift cost is more suitable to explore cross-talk of BLC and EC. Next, we do find cross-talk for the n-1 shift cost as demonstrated by a significant cross-domain correlation. This suggests that there are at least some shared processes in the linguistic and non-linguistic task.