In order to determine whether a bond is ionic or covalent, you need to know whether or not it is completely composed of nonmetal atoms or both metal and nonmetal ions.
Barium is a metal and Oxygen is a nonmetal, therefore there is no possible way they could bond unless they were attracted to opposite charges. Specifically, only if Barium becomes a cation and Oxygen becomes an anion then could they bond.
Now cation and anion both have the word "ion" in them, so therefore it must be an ionic bond.
Now we need to know the definition of a bond. A bond is formed when two elements are joined together by sharing their valence electrons.
Therefore, your answer should be:
Ionic, because valence electrons are shared.