An increasing body of research has investigated how bilingual language experience changes brain structure and function, including changes to task-free, or “resting-state” brain connectivity. Such findings provide important evidence about how the brain continues to be shaped by different language experiences throughout the lifespan. The neural effects of bilingual language experience can provide evidence about the additional processing demands placed on the linguistic and/or executive systems by dual-language use. While considerable research has used MRI to examine where these changes occur, such methods cannot reveal the temporal dynamics of functioning brain networks at rest. The current study used data from task-free EEGS to disentangle how the linguistic and cognitive demands of bilingual language use impact brain functioning. Data analyzed from 106 bilinguals and 91 monolinguals revealed that bilinguals had greater alpha power, and significantly greater and broader coherence in the alpha and beta frequency ranges than monolinguals. Follow-up analyses showed that higher alpha was related to language control: more second-language use, higher native-language proficiency, and earlier age of second-language acquisition. Bilateral beta power was related to native-language proficiency, whereas theta was related to native-language proficiency only in left-hemisphere electrodes. The results contribute to our understanding of how the linguistic and cognitive requirements of dual-language use shape intrinsic brain activity, and what the broader implications for information processing may be.