We developed a novel hybrid population balance-Brownian dynamics (Pop-BD) simulation technique to investigate the phase behavior and linear viscoelastic response of suspensions of colloids bridged reversibly by telechelic polymers such as latex particles bridged by polyethylene oxide urethanes. The Pop-BD method couples the solution of a set of population balance equations of the bridge-to-loop exchange kinetics of the telechelic polymer chains on the latex particles with Brownian dynamics simulations governing the dynamics of the latex particles. Two relaxation times are identified, corresponding to bridge association/dissociation from the latex particle and relaxation of the transient network of bridged particles. The relaxation modulus computed from the Pop-BD equations matches that for fully explicit BD simulations of both colloids and polymers at time scales equal to or greater than the polymer bridge relaxation time. (C) 2017 The Society of Rheology.