We investigate the effects of competing bulk and surface fields on the adsorption of near-critical fluids confined in model pores. Our study is motivated by recent measurements for SF6 adsorbed in a mesoporous glass which showed the phenomenon of critical depletion in that the adsorption excess first increases but then decreases rapidly to negative values as the temperature approaches the bulk critical temperature from above, following a near-critical isochore. We argue on the basis of (i) critical scaling ideas, (ii) exact transfer matrix calculations in two dimensions, and (iii) mean-field calculations, for the lattice gas confined between two planar walls, that critical depletion is a general phenomenon resulting from competition between positive adsorption (the walls or surface fields favor the dense liquid phase) and negative adsorption associated with the presence of a bulk field which favors the dilute gas phase. The temperature at which crossover from critical adsorption, of the type associated with a single wall, to depletion, depends on the magnitude of the bulk field and the width of the pore, and we identify the appropriate scaling relations. We discuss the extent to which results for our idealized model can account for the experimental observations and how; these relate to the results of computer simulations of a Lennard-Jones fluid in a planar slit.