When reading, proficient bilinguals seem to engage the same cognitive circuits regardless of the language in use. Yet, whether or not such “bilingual” mechanisms would be lateralized in the same way in distinct—single or dual—language contexts is a question for debate. To fill this gap, we tested 18 highly proficient Polish (L1) —English (L2) childhood bilinguals whose task was to read aloud one of the two laterally presented action verbs, one stimulus per visual half field. While in the single-language blocks only L1 or L2 words were shown, in the subsequent mixed-language blocks words from both languages were concurrently displayed. All stimuli were presented for 217 ms followed by masks in which letters were replaced with hash marks. Since in non-simultaneous bilinguals the control of language, skilled actions (including reading), and representations of action concepts are typically left lateralized, the vast majority of our participants showed the expected, significant right visual field advantage for L1 and L2, both for accuracy and response times. The observed effects were nevertheless associated with substantial variability in the strength of the lateralization of the mechanisms involved. Moreover, although it could be predicted that participants' performance should be better in a single-language context, accuracy was significantly higher and response times were significantly shorter in a dual-language context, irrespective of the language tested. Finally, for both accuracy and response times, there were significant positive correlations between the laterality indices (LIs) of both languages independent of the context, with a significantly greater left-sided advantage for L1 vs. L2 in the mixed-language blocks, based on LIs calculated for response times. Thus, despite similar representations of the two languages in the bilingual brain, these results also point to the functional separation of L1 and L2 in the dual-language context.