In its Campaign 9, K2 observed dense regions toward the Galactic bulge in order to constrain the microlensing parallaxes and probe for free-floating planets. Photometric reduction of the K2 bulge data poses a significant challenge due to a combination of the very high stellar density, large pixels of the Kepler camera, and the pointing drift of the spacecraft. Here we present a new method to extract K2 photometry in dense stellar regions. We extended the Causal Pixel Model developed for less-crowded fields, first by using the pixel response function together with accurate astrometric grids, second by combining signals from a few pixels, and third by simultaneously fitting for an astrophysical model. We tested the method on two microlensing events and a long-period eclipsing binary. The extracted K2 photometry is an order of magnitude more precise than the photometry from other method.