Earlier this week, Bradley said he's had to deal with "adversity and hatred," and not just at Wrigley Field but also at restaurants.
Williams, 71, could only address the baseball side, and said he hoped Wrigley Field ushers would remove anyone making derogatory remarks to the players. Cubs security has not reported anything unusual in the right-field bleachers regarding Bradley.
"I'll say this, the fans want you to perform," Williams said. "They want you to perform because you have that title of 'Major League Baseball player' and they expect that and they have a right to boo if you're not performing. They expect you to perform."
Williams said he didn't know of any specific instances at Wrigley that set Bradley off.
"I'm not in right field [with him]," Williams said. "I don't know what is said, what is not said. I know if you're in the ballpark and a public place like this, and those kind of remarks, those derogatory remarks, are directed to any player, the ushers have a job to get those people out of here."
He may not be in right field, but Williams did play left during some racially turbulent times.
"I didn't hear any derogatory remarks," Williams said. "When you weren't swinging a bat real good -- and I didn't do that too often -- you'd hear people who would say things that you wouldn't appreciate. I was big enough at that time to let it slide over. The derogatory remarks, I didn't hear."
The sense he gets, Williams said, is fans are focused on what players do on the field and they don't care about race or your family tree.
"Here's a case of a player who played here and had some good years -- Randy Hundley -- and his son [Todd] came here and didn't do so well and he got booed," Williams said. "It's not directed to any player who's doing good, it's directed to players who aren't having a good year. The fans just want to see good baseball.
"Because we've made the playoffs the last couple years, they want a winner here," he said. "If you don't perform, they say, 'Hey, he's in the Major Leagues and he should perform.'"
Cubs first baseman Derrek Lee told Bradley the best thing to do is ignore the comments. Williams agrees.
"You've got to have confidence that you can get beyond that," Williams said. "Those people have a problem. You have to be like a duck out of water -- you have to let it flow off your back."
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.