Language experience shapes infants' abilities to process speech sounds, with universal phonetic discrimination abilities narrowing in the second half of the first year. Brain measures reveal a corresponding change in neural discrimination as the infant brain becomes selectively sensitive to its native language(s). Whether and how bilingual experience alters the transition to native language specific phonetic discrimination is important both theoretically and from a practical standpoint. Using whole head magnetoencephalography (MEG), we examined brain responses to Spanish and English syllables in Spanish‐English bilingual and English monolingual 11‐month‐old infants. Monolingual infants showed sensitivity to English, while bilingual infants were sensitive to both languages. Neural responses indicate that the dual sensitivity of the bilingual brain is achieved by a slower transition from acoustic to phonetic sound analysis, an adaptive and advantageous response to increased variability in language input. Bilingual neural responses extend into the prefrontal and orbitofrontal cortex, which may be related to their previously described bilingual advantage in executive function skills. A video abstract of this article can be viewed at: https://youtu.be/TAYhj‐gekqw