You can get plenty of influence with Mira aboard the Hawk. You need to have a high enough Wisdom, Awareness or Intelligence check though. When you ask her about her famiily, you can hit on a check that gives you a option to comment on how she works as a bounty hunter because she's never been able to find her own family. She'll get angry and tell you to go away, but you get influence from this. Talk to her again, and apologize-you'll end up with more.
I've gotten to the point I can turn her into a Jedi without ever leaving Nar Shadaa.
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Do you know how high the wisdom, intelligence, and/or awarness has to be?