The Brown Bunny

Motorcycle racer Bud Clay undertakes a cross-country drive, following a race in New Hampshire, in order to participate in a race in California. All the while he is haunted by memories of his former lover, Daisy. On his journey he meets three women, but Bud seems to be a lost soul, and he is unable to form an emotional connection with any of them. He first meets Violet at a gas station in New Hampshire and convinces her to join him on his trip. They stop at her home in order to get her clothes, but he drives off as soon as she enters the house.
Bud's next stop is the home of Daisy's parents, the location of Daisy's brown bunny. Daisy's mother does not remember Bud, who grew up in the house next door, nor does she remember having visited Bud and Daisy in California. Next, Bud stops at a pet shelter, where he asks about the life expectancy of rabbits (he is told it is about five or six years). At a highway rest stop, he meets a distressed woman, Lilly. He comforts and kisses her, before starting to cry and eventually leaving her. Bud appears more distressed as the road trip continues, crying as he drives. He stops at the Bonneville Speedway to race his motorcycle. In Las Vegas, he drives around prostitutes on street corners, before deciding to ask one of them, Rose, to join him for a lunch. She eats McDonald's food in his truck until he stops, pays her, and leaves her back on the street.
After having his motorcycle checked in a Los Angeles garage, Bud stops at Daisy's house, which appears abandoned. He leaves a note on the door frame, after sitting in his truck in the driveway remembering about kissing Daisy in this place, and checks in at a hotel. Daisy eventually appears there. She seems nervous, going to the bathroom twice to smoke crack cocaine, while Bud waits for her, sitting on his bed. As she proposes to go out to buy something to drink, Bud tells her that, because of what happened the last time they saw each other, he does not drink anymore.
They have an argument about Daisy kissing other men. At this point, Bud undresses Daisy and she performs fellatio on him, culminating in her swallowing his semen. Once done, he insults her as they lie in bed, talking about what happened during their last meeting. Bud continuously asks Daisy why she had been involved with some men at a party. She explains that she was just being friendly and wanted to smoke marijuana with them. Bud becomes upset because Daisy was pregnant and it transpires that the baby died as a result of what happened at this party.
Through flashback scenes, the viewer understands that Daisy was raped at the party, a scene witnessed by Bud, who did not intervene. Daisy asks Bud why he didn't help her, and his feelings of guilt on this are considerable. He tells her that he did not know what to do, and so he decided to leave the party. After he came back a bit later, he saw an ambulance in front of the house and Daisy explains to Bud that she is dead, having passed out prior to the rape and then choked to death on her own vomit. Bud awakens the next morning, alone; his encounter with Daisy turns out to have been a figment of his imagination. The movie ends as Bud is driving his truck in California.

Question: Who joined Bud for lunch?
Answer: Rose/prostitute.