Palette coding has been adopted in the draft standard of HEVC screen content coding (HEVC SCC). This paper shows that a considerable portion of areas in screen visual contents typically contains two major colors. Therefore, this paper proposes two bi-color coding tools, called bi-color index coding (BCIC) and bi-color prediction mode (BCPM). The BCIC addresses the bi-color coding issue within the palette mode by enhancing the index coding for bi-color indices. The BCPM, however, is an independent mode that performs bi-color prediction for the current coding unit by a candidate list of previously decoded pixels. The resulting indices are binary that can be effectively coded by the proposed BCIC. Both of the BCIC and BCPM have been recommended to be further studied in the core experiments of HEVC SCC in the 18th JCT-VC meeting. Experimental results show that the BCIC and BCPM improve the BD-rate saving of SCM1.0 up to -1.3% and -2.9% respectively.