The theory of infite-dimensional systems introduced and developed by Salamon [Trans. Amer. Math. Soc., 300 (1987), pp. 383-431] and Weiss [SIAM J. Control Optim., 27 (1989), pp. 527-545] has been recently applied for various systems; see, e. g., the Jacob-Partington survey [Current Trends in Operator Theory and its Applications, Birkhauser, Boston, 2004]. In the same spirit, Schnaubelt, in his recent work [SIAM J. Control Optim., 41 (2002), pp. 1141-1165], has extended their approach to the time-varying linear systems. In this paper, we follow this spirit and prove that one can extend the results recently obtained for infite-dimensional time-invariant bilinear systems to the time-varying setting. In particular, we show that the absolute regularity and detectability assumptions ensure the existence of an observer for this kind of systems.