Now that's interesting!
Some things to ponder, though:
I wonder who would run in the Democratic primaries. Would there have been candidates running already when he entered the race or did many sit it out once a Bill'04 became an early presumption. I think Dean would still run, but Kerry might sit it out, maybe.
Actually, was Clinton even popular enough IOTL in 2002/2003 to pull off such a run? He'd have to have enough support to win the nomination.
Also, whom would he pick to be his running mate? Dean? Kerry? Edwards? Barbara Boxer? Bob Graham? Gary Locke? Evan Bayh? (I really don't know).
How would such a campaign work with his wife currently serving in the US Senate?
Bill Clinton had health issues in 2005. Would they been worsened by a 2003-2004 campaign and occur in the fall campaign?
One more thing, I can easily see GWB simply bringing up Monica, or even accusing the Clinton administration of dropping the ball when it came to foreign policy and causing 9/11 to eventually occur.
Personally, I think it would be a very narrow race, maybe even closer than OTL's 2004, but ultimately GWB would win re-election.