Recently, random graph theory has been extensively applied in biological networks, chemical networks, and physical processes. They can provide meaningful insights into the structure of a network. Numerous studies have been conducted on studying degree-based graph and investigating their properties, among which the first Zagreb index, the second Zagreb index, and the Forgotten index are the most important ones. Two famous models of random graphs are the Erdös-Rényi random graph models, on which extensive research has been carried out. Among these, finding and determining the limits of topological indices in various models of random graphs is of particular interest. Therefore, multiple efforts have been made to study the limits of these indices in Erdös-Rényi random graphs. In this paper, we focus on investigating graph invariants for inhomogeneous bipartite random graphs. Accordingly, we first compute the expected value of the first Zagreb index for inhomogeneous bipartite random graphs. Similarly, we examine the expected values of the second Zagreb index and the Forgotten index for inhomogeneous bipartite random graphs. Furthermore, by establishing upper and lower bounds for the probabilities of edge occurrences, the expected value bounds for these indices in inhomogeneous bipartite random graphs are determined. These analyses contribute to a better understanding of the properties of random graphs.