This paper presents a fast and accurate approximation of the bilateral filter for color images such as medical color images. The bilateral filter has a problem of high computational complexity. Various acceleration methods have been proposed in the past. However, most of the existing methods have been developed for grayscale images, not for color images. Therefore, the computational complexity is high even though we apply the state-of-the-art fast approximate methods to color images. This paper tackles the problem based on the idea of the cross/joint bilateral filter. It filters a target image using an additional guide image for higher-quality output. Our key idea is to generate the guide image by the principal component analysis for the color vector distribution of the target image. As a result, the proposed method achieves highly-accurate approximation of the bilateral filter and succeeds in drastically reducing the computational complexity. Our experiments show that the proposed method is robust in high contrast medical color images. Furthermore, we combined the state-of-the-art constant-time bilateral filter with the proposed method. This combination achieved high quality performance in terms of both approximate accuracy and computational complexity.