Westwood has not played competitively in two months because of his calf problem, with his last tournament the BridgestoneInvitational back in early August.
Bradley, who won last weekend's WGC-Bridgestone Invitational as Woods tied for eighth, has been followed by this year's Masters winner Bubba Watson and U.S. Open champion Webb Simpson.
The 14-time major champion can topple Luke Donald by winning the World Golf Championships-Bridgestone Invitational tournament for the eighth time as long as the Englishman finishes no higher than third come Sunday.
Last week's BridgestoneInvitational winner Adam Scott is among three players just three shots off the lead, while world No.2 Lee Westwood is four off the pace after a 68 and world No.1 Luke Donald is six behind after carding a 71.