The quest becomes available at 50% friendship or rivalry.
Isabela will finish a card game with Merrill and speak to you about her outlook on you thus far. You will get three dialogue options, with the first and third each having the standard Good/Witty/Angry options for answers. The second one, however, will have a Flirt option as the middle option. Note that flirting with Isabela here can initiate a romance.
In a friendship, Isabela will invite Hawke to sit, ordering the Hanged Man's best whiskey for him/her.
- Diplomatic: "Thank you."
- Humorous: "That's not all."
- Aggressive: "Save your money."
She will then comment on how Hawke "doesn't judge people."
- Diplomatic: "How so?"
- Flirt: "Just all right?"
- Aggressive: "I don't need your approval."
Finally, she will talk about how if you were part of her crew, she wouldn't have gotten shipwrecked.
- Diplomatic: "It all worked out."
- Humorous: "I wouldn't bet on it."
- Aggressive: "Don't dwell on the past."
Under a Rivalry, Isabela will be much more catty and wonder why Hawke is visiting her, snarking that there's a "burning orphanage full of children to save."
- Diplomatic: "Is there?"
- Humorous: "Of course!"
- Aggressive: "No."
She'll talk about Hawke missing the joke, and states that he/she needs to learn how to have fun like her.
- Diplomatic: "Life's not all fun and games."
- Humorous: "I enjoy life just fine."
- Aggressive: "I'm not you."
Finally, she'll state that "We're not responsible for anyone but ourselves. You can choose to be free, or you can choose to be saddled with all the world's problems."
- 1: "You're not free."
- 2: "Helping others benefits me."
- 3: "Helping others is rewarding."
Regardless of your choice, she will dismiss your rationale, ending with, "We're done here. Talking to you is exhausting, and not much fun."
If you have a friendship with Isabela then on the first dialogue option if you choose the diplomatic or humorous option Isabela: friendship (+20), and Isabela: friendship (+10) if you choose the aggressive option (it does not matter what you choose on the second and third dialogue options).
If this quest is completed and Hawke has at least 50% friendship/rivalry with her, Isabela will subsequently show up when she is least expected.