Bose condensation in 2D quasiparticle systems is considered within a microscopic model. With the help of the Schwinger-Keldysh formalism, the mean-field dynamical equations are derived. We show that the main features of condensate interactions with reservoirs of non-condensable particles can be captured by simple memory terms with exponential kernels. By analyzing the steady-state solution of this equation, we obtain the phase diagram of the quasiparticle gas and find the bistability region in the parameter space of the system. Finally, as an application of our theory, we examine the phase diagram for exciton-polariton condensates.