Short answer: He didn't. (Even ignoring the Florida mess, fewer people voted for Bush than Gore).
Right, because we all know the popular vote determines who wins an election.
We also know what's the definition of democracy. Except for in South Carolina of course. What's called "democracy" in US (electoral college) would be called dictatorship or at best quasi-dictatorship in about 90% of the other nations of the world, including 100% of Western Europe.
Which has nothing to do with the fact that under our voting system, Bush won. Unless you mean he won the election in the sense that in a true democracy he would have, but the United States is not a true democracy.