We developed a novel data-driven Artificial Intelligence-enhanced Adaptive Time Stepping algorithm (AI-ATS) that can adapt timestep sizes to underlying biophysical dynamics. We demonstrated its values in solving a complex biophysical problem, at multiple spatiotemporal scales, that describes platelet dynamics in shear blood flow. In order to achieve a significant speedup of this computationally demanding problem, we integrated a framework of novel AI algorithms into the solution of the platelet dynamics equations. Our framework involves recurrent neural network-based autoencoders by the Long Short-Term Memory and the Gated Recurrent Units as the first step for memorizing the dynamic states in long-term dependencies for the input time series, followed by two fully-connected neural networks to optimize timestep sizes and step jumps. The computational efficiency of our AI-ATS is underscored by assessing the accuracy and speed of a multiscale simulation of the platelet with the standard time stepping algorithm (STS). By adapting the timestep size, our AI-ATS guides the omission of multiple redundant time steps without sacrificing significant accuracy of the dynamics. Compared to the STS, our AI-ATS achieved a reduction of 40% unnecessary calculations while bounding the errors of mechanical and thermodynamic properties to 3%.