I recall Rove being an adviser to Bush, but never a 'spokesman.' Bush's spokespersons were Karen Hughes, Ari Flischer, Tony Snow (God rest his soul) and that really incompetent Scott McClellan. All were pretty good other than McClellan who was in way over his head.
As to not responding to some of the mud slung by the democrats, that was Bush's style. He refused to get down in the mud. He wanted to keep it classy. I don't think it is fair to 'blame' the lack of response on anyone but Bush.
Karen Hughes was not a spoke person for President Bush. She was his his director for his campaign for the office of Governor of Texas. and then as a counselor from 2001 to 2002, while he was President of the United States.
Hughes left the Bush administration in July 2002 to return to Texas, but remained in daily contact with the Bush reelection campaign by telephone and e-mail, and spoke personally with Bush several times a week. In August 2004, Hughes returned to full-time service with the Bush campaign, setting up office on Air Force One, from where she planned the 2004 Republican National Convention and the late stages of the 2004 election.
President Bush's spokespersons (Press secretaries) were in order
Ari Fleischer
Scott McClellan
Tony Snow
Dana Perino