I will not be made to hide!"
In addition to being headstrong and determined, Ashe also has a very strong sense of justice and righteousness. She quickly corrects anyone who calls the resistance an "insurgence" and is scandalized when soldiers mistake her for a thief after escaping with Vaan, Balthier, and Fran's aid. She is a bit aloof, but it seems only natural that she would want to preserve her dignity after all the injustices that she suffered. Ashe's harsh personality is especially surprising considering her elegant design and status as Princess, but it's an outlook that she really has to take on. She faces an entire empire and its ruthless leader, a world that thinks she is dead, no evidence of her lineage, and harbors a deep hatred of the forces that claimed the lives of her husband and father which she can't put behind her. So it makes sense that she has such a solid resolve. I think these aspects of her character surprised a lot of people, since I don't think many players expected her to be so harsh, cold, and commanding. Call her mean or rude all you want, but her attitude is justified when you think about her situation. As Vossler states at one point, "her Majesty cannot abide weakness, least of all in herself."
This rather icy determination and insistence on going about things her way lands Ashe in a bit of a predicament at times when her strong will clouds her judgment. When seeking help from Ondore in Bhujerba, her wishes are refused as Ondore wants to keep her safe in hiding. Ashe shows a bit of recklessness thereafter, when she attempts to fly off with the Strahl by herself (while Vaan, wonderfully blunt as usual, asks her if she's crazy. And really, it's a valid question, seeing as the walls in Raithwall's Tomb? WILL KILL YOU.). After Balthier finds her, she asks the sky pirate to kidnap her, further proof that she'll really do whatever it takes.
I don't want to say that Ashe "softens" during the course of the game, because she remains just as determined and strong up through the final battle. But we do see her warm to her companions as she travels alongside them. From realizing the similarities between her ordeal and Vaan's to her outright concern for Balthier's wellbeing as he stays behind on the Bahamut, it's clear that she comes to appreciate the "common thieves" and traitors who she didn't want anything to do with when she first met them. Unlikely allies become the most trusted of friends, regardless of occupation, social status, or supposed treason. Forming these relationships seems to lead Ashe to some realizations about herself; at the end of game she speaks her infamous line, "I am simply myself." It doesn't matter if she's a princess, she has the right to be free and follow her own path regardless of her status, as does everyone else.
Ashe's past or childhood isn't explored in-depth during the game. We don't really know if Ashe's mostly harsh nature began when she went underground or if she was always that aloof, but she appears to have been fairly happy and content prior to the game in the few cutscenes we see. Like I've detailed here, we do get a glimpse of some tender moments between her and Rasler. During the credits, we see an image of a smiling young Ashe with a Chocobo. It looks like she had an innocent and comfortable life prior to Dalmasca's fall and the war. Whether her personality was different during this time is unknown.