Interestingly enough Bush Sr., Reagan, and even Bob Dole in 1996 won the Asian vote.
I think a lot of that has to do with the inner-city riots that took place in the 1980s and early 1990s. Particularly after the Rodney King incident, there were a lot of Asian-owned stores and restaurants that got damaged and ransacked by the black rioters. Add to that the fact that Asians generally view black people as not entirely civilized (this is true both among Asian-Americans and among Asians in Asia), and they likely wanted to vote for the party they associated with "law and order" and against the party that blacks tended to support.
I had been told that Dole won the Asian vote and also that it had something to do with Vietnam (and of course the war). When I stumbled onto Steve Gunderson's page, I began to get an idea as to why. Apparently, the Clinton administration had tried to repatriate the Laotian Hmong, who had been our allies during the Vietnam War and folks like Gunderson (praised by conservatives for it) stood against it. So that gives me some idea as to why Asians used to vote Republican.