The bilingual executive advantage (BEA) hypothesis has attracted considerable research interest, but the findings are inconclusive. We addressed this issue in the domain of working memory (WM), as more complex WM tasks have been underrepresented in the previous literature. First, we compared early and late bilingual vs. monolingual WM performance. Second, we examined whether certain aspects of bilingual experience, such as language switching frequency, are related to bilinguals' WM scores. Our online sample included 485 participants. They filled in an extensive questionnaire including background factors such as bilingualism and second language (L2) use, and performed 10 isomorphic verbal and visuospatial WM tasks that yielded three WM composite scores (visuospatial WM, verbal WM, n-back). For verbal and visuospatial WM composites, the group comparisons did not support the BEA hypothesis. N-back analysis showed an advantage of late bilinguals over monolinguals and early bilinguals, while the latter two groups did not differ. This between-groups analysis was followed by a regression analysis relating features of bilingual experience to n-back performance, but the results were non-significant in both bilingual groups. In sum, group differences supporting the BEA hypothesis were limited only to the n-back composite, and this composite was not predicted by bilingualism-related features. Moreover, Bayesian analyses did not give consistent support for the BEA hypothesis. Possible reasons for the failure to find support for the BEA hypothesis are discussed.