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In 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range of applications. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> be the class of bipartite graphs of order <i>n</i> and diameter <i>d</i>. In this paper, we mainly characterize the bipartite graphs in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> with the maximal inverse sum indeg index. Bipartite graphs with the largest, second-largest, and smallest inverse sum indeg indexes are also completely characterized.