If we are taking ' to go out with you' as meaning to go out on a date etc, then probably the second one is the most universally used phrase in this situation.
However there are many exceptions to the rule, mostly based on the context that one might find oneself in when having such a conversation.
SENTENCE 1 "She is reluctant to go out with you" ..............The use of the word reluctant suggest that she has reservations, maybe because she has heard things about the way this person (who might be charming and handsome etc) treats other people. So in the context of the question .....Does she want to go out with me sometime, it is a MAYBE.
SENTENCE 3: She is unwilling to go out with you.............. Same as sentence 1, but this time, the reasons not to go out with this person are more serious. Possibly the person is doing things that she disagrees with on ethical grounds or the person has hurt one of her friends in the past. Could be anything, but this response is a very clear NO and it would appear to be based on some past experience.
To say that to a stranger based on say their looks alone would be pretty rude and quite unlikely so it is more than likely to be a response based on some past history.
In terms of sending a clear, (to a certain degree polite) and unambiguous response, Sentence 2 is most likely best.
Hope that helps.