A woman in a wedding dress, the Bride, lies wounded in a chapel in El Paso, having been attacked by the Deadly Viper Assassination Squad. She tells their leader, Bill, that she is carrying his baby. He shoots her.
Four years later, having survived the attack, the Bride goes to the home of Vernita Green, planning to kill her. Both women were members of the Deadly Viper Assassination Squad, which has since disbanded; Vernita now leads a normal suburban family life. They engage in a knife fight, but are interrupted by the arrival of Vernita's young daughter, Nikki. Not wanting to kill Vernita in front of Nikki, the Bride agrees to meet Vernita at night to settle the matter, but Vernita tries to surprise the Bride with a pistol hidden in a box of cereal. The Bride dodges the shot and throws a knife into Vernita's chest, killing her.
Four and a half years earlier, police investigate the massacre at the wedding chapel. The sheriff discovers the Bride is alive but comatose. In the hospital, Deadly Viper Elle Driver prepares to assassinate the Bride via lethal injection, but Bill aborts the mission at the last moment, considering it dishonorable to kill the Bride when she cannot defend herself.
In the present, the Bride awakens from her four-year coma and is horrified to find she is no longer pregnant. She kills a hospital worker who has been raping her while she was comatose, takes his truck, and teaches herself to walk again. Resolving to kill Bill and all four members of the Deadly Viper Assassination Squad, she picks her first target: O-Ren Ishii, now the leader of the Tokyo yakuza. O-Ren's parents were murdered by the yakuza when she was a child; she took vengeance on the yakuza boss and replaced him after training as an elite assassin.
The Bride travels to Okinawa, Japan, to obtain a sword from legendary swordsmith Hattori HanzĹ, who has sworn never to forge a sword again. After learning that her target is Bill, his former student, he forges his finest sword for her. The Bride tracks down O-Ren at a Tokyo restaurant, the House of Blue Leaves, and defeats her yakuza army, including the elite Crazy 88 and O-Ren's bodyguard, schoolgirl Gogo Yubari. She duels with O-Ren in the restaurant's Japanese garden. During the duel O-Ren apologizes to the Bride, who tearfully accepts. They continue and the Bride slices O-Ren's scalp off with a sword stroke. Afterwards, she tortures Sofie Fatale, O-Ren's assistant and Bill's protege, for information about Bill, and leaves her alive as a threat. Bill asks Sofie if the Bride knows her daughter is alive.

Question: Why does the bride agree to fight Vernita Green at a later time?
Answer: Because she does not want to kill Vernita Green in front of her daughter 
Alternative answer: To not kill her in front of her young daughter.