Rates of land surface processes provide insights into climate and tectonic influences on landscape dynamics. River incision rates into bedrock are estimated by dating perched landforms such as strath terraces, assuming a constant bedrock incision rate from terrace abandonment to present. These estimates express biases from the stochastic nature of river incision and from using a mobile channel elevation as a reference frame. No existing mechanistic framework fully addresses these biases. We introduce a 1-D river evolution model incorporating fluvial mechanics, sediment dynamics, tectonics, and climatic factors to predict these biases and assess their sensitivity to climate and rock-uplift rate. Findings suggest biases intensify under highly variable climates and slow rock uplift, with the period of climate being a primary control. Our model improves river incision measurement reliability, impacting paleoclimate and tectonic geomorphology reconstructions.