The bridge just may be Confucianism---the dialogue between cultures could benefit from it's universal messages and it so happens that there has been a recent popularization of Confucianism. Is this by chance or is it the natural order of things? I believe the time has come for this philosophy to make a global impact.
What Confucian thought can do is put light on the fact that there is no pure Western civilization or pure Chinese civilization. East is in the West and vice versa and this is how it's always been in reality.....because issues are universal.
The dialogue is not between civilizations but inside civilization.