This paper presents a doubly dynamic day-to-day (DTD) traffic assignment model with simultaneous route-and-departure-time (SRDT) choices while incorporating incomplete and imperfect information as well as bounded rationality. Two SRDT choice models are proposed to incorporate imperfect travel information: One based on multinomial Logit (MNL) model and the other on sequential, mixed multinomial/nested Logit model. These two variants, serving as base models, are further extended with two features: bounded rationality (BR) and information sharing. BR is considered by incorporating the indifference band into the random utility component of the MNL model, forming a BR-based DTD stochastic model. A macroscopic model of travel information sharing is integrated into the DTD dynamics to account for the impact of incomplete information on travelers’ SRDT choices. These DTD choice models are combined with within-day dynamics following the Lighthill-Whitham-Richards (LWR) fluid dynamic network loading model. Simulations on large-scale networks (Anaheim) illustrate the interactions between users’ adaptive decision making and network conditions (including local disruption) with different levels of information availability and user behavior. Our findings highlight the need for modeling network transient and disequilibriated states, which are often overlooked in equilibrium-constrained network design and optimization. The MATLAB package and computational examples are available at https://github.com/DrKeHan/DTD.