Williams, seeded 12th, notched her third successive one-sided victory as she takes aim at following her Wimbledon triumph with a third U.S. Open crown.
"I just want to take that experience from Wimbledon and bring it here," the 27-year-old Williams said in a courtside interview.
"I've done it a couple of times here before and I want to do it again."
Williams dispatched 21st seed Bondarenko with 30 winners, despite getting only 51 percent of her first serves in.
"I definitely would like to have a higher first-serve percentage, but it's not something I'm worried about," she said. "I still feel like I can get my serve in. My second serve nowadays has a lot of kick. So it was a good day."
Williams, who won the Open in 2000 and 2001, showed a lot of fire with her service returns.
"It's just coming," said Williams, oozing confidence. "I know I'm going to go for it. It's nice that it comes naturally."
In contrast to her sister, Serena, another two-times U.S. Open winner who has struggled through her first three matches this year, Venus is playing loose and free.
"I just feel like I win all the important points and that really makes a big difference in how my opponent feels playing against me and how I feel about the match, too," she said.
Venus said she was not worried about younger sister Serena, who she described as "an unbelievable competitor".
"When push comes to shove, she shoves," Venus said with a smile.
Waiting for Venus in the round-of-16 will be fifth-seeded Ana Ivanovic of Serbia, a decisive 6-1 6-3 winner against Russian Vera Dushevina.
Williams, who has a 3-0 career record against the 19-year-old Ivanovic, beat the Serbian 6-2 6-4 in the semi-finals at Wimbledon on her way to the title.
