I see the purpose of Diane's dream as Diane (as Betty -- her good side -- her imagined or exaggerated inner strengths, idealized) needing to fall in love with her dark side (the angry, jealous side that has also committed murder). And that this might even save her from suicidal depression.
Diane has to fully accept herself -- come to terms with herself; to fall in love with herself. And the only way she can do this is to create a dark half that is lovable to her -- a Camilla look-alike: Rita. But for the dream to succeed, Rita has to love her back. And this fails.
Diane-as-Betty falls in love with Rita but Rita (in bed) doesn't return her expressions of love; and this is a crucial point -- the point where Diane's dream starts to come apart. And I mean almost right away -- Camilla is now in control as she practically drags Betty off to Club Silencio. Even in the cab ride to Silencio, Betty for the first time looks lost and confused -- out of control; more like Diane.
Rita IS the Bum behind Winkie's -- Rita is Diane's dark half all dressed up and made lovable (for reasons stated above). The raw, stark form of Diane's dark half is the Bum.

Theory Threads:
The Dual Nature of Diane's Dream

Other Threads:
Naomi's interpretation...
Mulholland Drive: A Philosophical Treatise
The "Wrapped in Plastic" Analysis of MD (I hope!)
Do we reduce the beauty of this work of art by analysis?
Naomi Watts, on shooting the audition scene...