Monte Carlo simulations of the fluctuating bond lattice model are used to determine the force between colloidal particles immersed in a nonadsorbing polymeric fluid. Monodisperse systems with chain lengths of 20 to 100 segments are studied at occupation fractions ranging from 0.1 to 0.6, covering the semidilute and dense regimes. The variation of the force with concentration, particle diameter, and interparticle separation is in qualitative agreement with predictions of scaling theory and of integral equations for the colloid-polymer system. In semidilute solutions the force is purely attractive and displays an approximately linear dependence upon separation for small colloid separations. At higher concentrations the force is repulsive, for certain separations.