In this paper, we propose a novel color constancy approach, called Bag of Color Features (BoCF), building upon Bag-of-Features pooling. The proposed method substantially reduces the number of parameters needed for illumination estimation. At the same time, the proposed method is consistent with the color constancy assumption stating that global spatial information is not relevant for illumination estimation and local information ( edges, etc.) is sufficient. Furthermore, BoCF is consistent with color constancy statistical approaches and can be interpreted as a learning-based generalization of many statistical approaches. To further improve the illumination estimation accuracy, we propose a novel attention mechanism for the BoCF model with two variants based on self-attention. BoCF approach and its variants achieve competitive, compared to the state of the art, results while requiring much fewer parameters on three benchmark datasets: ColorChecker RECommended, INTEL-TUT version 2, and NUS8.