Introduction: This article presents a novel approach to anomia therapy (i.e., BAbSANT: Bilingual Abstract Semantic Associative Network Training) for bilingual persons with aphasia (B-PWA) that capitalizes both on lexico-semantic theories in bilingualism and general theories of semantic organization and learning. Based on previous work, we hypothesized that training abstract words in either language would promote within-language generalization, while training in the nondominant language would promote both within- and cross-language generalization. Methods: This case study used a single-subject A1BA2CA3 design. The participant was living with aphasia secondary to stroke and spoke both Polish and English, with Polish being his native and dominant language. Phase B consisted of abstract word training in Polish and phase C consisted of abstract word training in English. Prior to initiating therapy, in addition to a comprehensive language battery, we administered a cognitive control task to explore the relationship between cognitive control and treatment outcome. Results: We found within-language generalization regardless of the trained language, replicating previous work in monolingual persons with aphasia, further supporting the utility of training abstract words. However, contrary to our second hypothesis, cross-language generalization only occurred when the stronger language was trained. Conclusions: The discussion of the results of this case study is framed within previous work and theories of bilingualism. The lack of cross-language generalization when the weaker language was trained is discussed, taking into account nonverbal cognitive control deficits. In addition to showing the efficacy of BAbSANT, these results highlight the importance of considering cognitive control as a factor influencing therapeutic outcomes in anomia treatment in bilingual PWA.