Bilingual experience may confer advantages in statistical language learning tasks. Given that SL tasks can measure different aspects of foreign language learning, which aspects benefit from bilingual experience is still largely unexplored. Here, we compared a Spanish monolingual and two (Spanish-Basque and Spanish-English) bilingual groups across three well-established SL tasks. Each task targeted a different aspect of foreign language learning as a proxy—i.e., word segmentation, morphological rule generalization, and word-referent learning. In Experiment 1, we manipulated sub-lexical phonotactic patterns to vary the difficulty of three SL tasks, and the results showed no differences between the groups in word segmentation. In Experiment 2, we included non-adjacent dependencies to target affixal morphology rule learning, and again there were no differences between the groups. Finally, Experiment 3 addressed word learning using a more challenging audio-visual SL task combining exclusive and multiple word-referent mappings. We observed a bilingual experience effect only for the exclusive mappings but not for the multiple mappings. These results suggest that bilingual experience might mainly exert influences on statistical language learning at the lexical level. We discuss these findings by contextualizing SL as a cognitive mechanism, an experimental task, and a proxy for foreign language learning, highlighting the strengths and limitations in detecting bilingual experience effects.