People have tried to ascribe a lot of symbolism to the bum behind Winkie's. But having seen MH again, I think what the homeless bum represents is pretty straightforward. It's yet another “identity switch” in Diane’s dream. By ID switch, if you notice, Diane keeps switching everyone's names and personalities around. The reason why she does this is that the dream keeps reminding her of her crime. Because everyone's names and faces are switched around, this fools her into not confronting what the dream keeps telling her.
In the case of Dan, in real life, he had been staring at her with a fearful look while she was also staring at him with fear. But in the dream, she made Dan take her place, then had his friend take Dan's place. But why?
Something about Dan's stare spooked Diane, and she became paranoid about him, like she imagined that he had either caught on to what she was doing, or that maybe he had remembered her face well enough to out her to the two detectives who were questioning everyone about Camilla's murder.
When she had the dream, she used Dan to symbolize her paranoia about him. However, instead of her being the one sitting at Winkie’s terrified of being found out, she made Dan terrified of the bum that lives behind the diner. When Dan approached the bum, she then killed him off (or made him faint) because she didn't want him to see what the bum was holding (the blue box, which symbolized the hit).
So, this part of the dream was a wish fulfillment fantasy. It was Diane hoping that if “Dan” figured her out, he died before he got the chance to help the detectives in their investigation. It was also an expression of her paranoia about him.