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The bandits will like you more if you're more submissive - submitting to them makes them happier with you in general.  Dominating them in general makes them less happy with you.

Once you've met him, you can also take missions from Jester to make the bandits like you more.

You can buy Drake Root at the merchant on the track, or from the witch's hunt in the swamp (during the day).

You can also throw love potions at the bandits during combat to make them like you more (unless that's been changed).