Bank lending dynamics are strongly influenced by internal adjustment mechanisms and accumulated risk exposure, both of which can contribute to financial instability if they are not properly managed. In this study, we propose a discrete-time banking monopoly model with delayed risk effects, in which the current lending decision depends on both current profitability and the previous-period loan portfolio. The delayed component is introduced to capture the economic impact of accumulated credit risk, regulatory capital pressure, and expected loss provisioning associated with loan expansion. Using a gradient-based bounded-rationality framework, the model was formulated as a two-dimensional, nonlinear map. We derive the equilibrium points and establish explicit local stability conditions using the Jury criterion. Furthermore, bifurcation analysis shows that the positive equilibrium may lose stability through flip and Neimark–Sacker bifurcations, depending on the interaction between the adjustment speed and the delayed risk intensity. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, isoperiodic diagrams, and basin-of-attraction plots, reveal rich nonlinear phenomena such as periodic oscillations, quasi-periodicity, and chaos. These results show that delayed risk exposure can be an endogenous cause of instability in the lending dynamics. It also outlines the role of prudential adjustment policies in ensuring stability in the banking sector.