You can get this quest at 1900 affection
The dialogue also branches off dependant on your choices.
(-> represents "goes to")
Choice 1:
[Flirt]Your mind is lovely: +40 [ -> Choice 2]
I can help: +40 [ -> Choice 3]
Just be careful: -2 [ -> Choice 3]
Choice 2:
[Flirt]And pretty:+40 [ -> Choice 4]
[Flirt]Do Jedi date?: +40 [ -> Choice 4]
Don't get cocky: 0 [ -> Choice 3]
Choice 3:
[Flirt] Can I be with you?: +40 [ -> Choice 4]
You chose this: -2
I guess I'd be uneasy too: -2 (although she reacts happily in the dialogue)
Choice 4:
I didn't mean to trouble you: 40
Don't go: 0
[Flirt]Are you sure?: 0
However, as said by romansamurai, as of 1.0.2 the reputation gain seems to be bugged, as you can see in the quest reward that you gain no affection with Ashara.
During the quest dialogue, you get the following affection gains:
Choice 1:
[Flirt]Your mind is lovely: +40
I can help: +40
Just be careful: -2
Choice 2:
[Flirt]And pretty:+40
[Flirt]Do Jedi date?: +40
Don't get cocky: 0
Choice 3:
I didn't mean to trouble you: 40
Don't go: 0
[Flirt]Are you sure?: 0
Total gain ranges from -2 affection to 120 affection depending on your choices.