If you choose not to use the accumulation buffer, acceptable results can be obtained by blending. Because of the subtraction step, you'll have to remap the color values to avoid negative results. Since the image values range from 0 to 1, the range of values after subtraction can be -1 (0 - 1) to 1 (1 - 0).
Scale and bias the bump map values to remap the results to the 0 to 1 range. Once you've made all three passes, it is safe to remap the values back to their original 0 to 1 range. This scaling and biasing, combined with fewer bits of color precision, make this method inferior to using the accumulation buffer.