PERSONALITY
The long and short of it is that Betrys never wanted to be the Herald of Andraste or the Inquisitor of anything. She doesn't mind politics--she wanted to go to the Conclave, after all--but her goals in life have always been simple. Marry, have children, and be the lady that House Trevelyan needs. Archery was a hobby of hers, not a career goal. If someone sat her down before the Conclave and ask her if she wanted to be any sort of political leader, she would have politely declined.
But no one did...and not only does Betrys do her duty when it's presented to her, she's a good Andrastian. She genuinely believes Andraste chose her, even after her second sojourn in the Fade. Likewise, she believes that what she chooses to do as Inquisitor will affect the fate of nations. Being a herald to the people is something she takes very seriously.
She's very conscious of her public face and spends a lot of energy being exactly as gently spoken as she's been taught a lady should be. When in doubt, she doesn't joke with strangers or show her irritation with them; her place, she believes, is to be a placid, calming presence, the herald that Andraste deserves. Moreover, she doesn't care to give strangers any more hold over her than she has to. Outbursts aren't a strength, nine times out of ten.
That biddable surface hides a woman with a core of steel, one who isn't afraid of making difficult decisions. When someone wrongs her, she doesn't hesitate to strike back with force. When criminals are brought to her throne for judgment, she shows little mercy. Betrys is someone who isn't afraid to condemn a man to death if she believes he deserves it. She's also incredibly stubborn when she feels others might be attempting to pull her in the wrong direction. For much of the course of the fight against Corypheus, she receives letter after letter from her parents, alternately pleading and demanding she return to Ostwick. She refuses every time, and her responses grow more quietly annoyed each time.
Among friends, she's much more open; with a gentleman for whom she's set her cap, she can be flirtatious. But until she's grown fond of a person, she tends to hold them at arm's length.
For better or worse, she's also very much a noble. While she cares for the people of Thedas, she places her duty to the Maker over her duty to the common person, and she's not particularly interested in shaking up the status quo.