Abstract: Blood clot formation involves the coupled processes of platelet aggregation and coagulation, which are triggered when there is break in a blood vessel. Platelet aggregation is largely a physical process while coagulation is biochemical, consisting of a large network of reactions that culminate in the generation of the enzyme thrombin. Thrombin cleaves fibrinogen into fibrin, which polymerizes into fibers to form a stabilizing gel matrix in and around growing platelet aggregates. Thrombin also (re)binds directly to fibrin but this interaction, and its purpose, is not fully understood. Thrombin-fibrin binding is often described as two independent, single-step binding events, one high-affinity and one low-affinity, each through a different exosite on thrombin. However, kinetic schemes describing these single-step binding events with reported kinetic rate constants cannot explain experimentally-observed residency times of fibrin-bound thrombin. In this work, we study a bivalent, sequential-step binding scheme as an alternative to the high-affinity event, and in addition to the low-affinity one. We developed mathematical models for the single- and sequential-step schemes consisting of reaction-diffusion equations to compare to each other and to previously published experimental data. We then used Bayesian inference, in the form of Markov Chain Monte Carlo, to learn model parameter distributions from the experimental data. For the model to best fit the data, we needed an additional assumption that thrombin was irreversibly sequestered; we hypothesized that this could be due to thrombin becoming physically trapped within fibrin fibers as they formed. We also discuss how our model can be used to further probe scenarios dealing with thrombin allostery.