Bivalirudin is used in patients with heparin-induced thrombocytopenia and is a direct thrombin inhibitor. Since it is a rarely used drug, clinical experience with its dosing is sparse. We develop a model that predicts the effect of bivalirudin, measured by the Partial Thromboplastin Time (PTT), based on its past fusion rates. We learn population-wide model parameters by solving a nonlinear optimization problem that uses a training set of patient data. More interestingly, we devise an adaptive algorithm based on the extended Kalman filter that can adapt model parameters to individual patients. The latter adaptive model emerges as the most promising as it reduces both the mean error and, drastically, the per-patient error variance. The model accuracy we demonstrate on actual patient measurements is sufficient to be useful in guiding optimal therapy.