Ethiopa is right across the Red Sea from Yemen. It is a short boat ride along an old trade rout. Getting to Libya is much harder because of the Sahara. And you seem to have forgotton the existence of Sudan and Egypt. The route to Libya is down the Nile and then across the coastal plain.
Ethiopia and Yemen were politically and culturally united for long periods in the past. The two names Sheba(Saba-Yemen)) and Ethiopia are almost interchangeable. There are Jews and Christians of ancient origin in both areas.