Reading efficiently in a second language (L2) is a crucial skill, but it is not universally achieved. Here we ask whether L2 reading efficiency is better captured as a language specific skill or whether it is mostly shared across L1 and L2, relying on general language abilities. To this end, we examined word frequency and predictability effects in sentence reading, and tested the same readers in L1 and L2, recording participants' eye-movements. Participants were 57 undergraduate bilingual speakers of Hebrew and English, languages that use different scripts, allowing for a clearer distinction between L1 and L2 processing. Both word frequency and word predictability effects were more pronounced in participants' L2 than in the L1, suggesting that both lower level and higher-order processes in reading are sensitive to language proficiency. Further, frequency effects in the L2 were linked with L2 proficiency but not general language abilities, and L2 predictability effects were not associated with either variable. Finally, readers' frequency and predictability effects in L1 and L2 were not associated with each other. Taken together, these results suggest that for different-script bilinguals, efficient reading in the L2 is a highly specific skill, dependent upon proficiency in that language, and drawing less on L1 and general language ability.