The official languages in Bosnia and Herzegovina are Bosnian, Serbian and Croatian, all three known as Serbo-Croatian as they are practically the same language. Serbo-Croatian is written in both Latin and in Cyrillic, making it the only Slavic language to officially use both scripts. In the Republika Srpska you'll see signs in Cyrillic, so a Serbian-English dictionary would be helpful there.
Variants among the Serbo-Croatian language differ only in the most academic of venues and also in traditional homes. There are different versions of the language throughout the area and spoken language changes between regions. However, the vocabulary differences are only cosmetic and do not hinder communication between Orthodox Serbs, Catholic Croats and Bosnian Muslims.
Many Bosnians speak English, as well as German owing to family connections as well tourism in former Yugoslavia before the war. Some older people are also able to speak Russian, as it was taught in schools during the communist era.