M.S.
It almost sounds like the flap at the top of the esphogus is not closing correctly; especially since there isn't a lot of bile, just some. This is what happens to baby who had GERD most of the time. Usually, they outgrow it, as my son and sister did, but I know some don't.
She needs a different opinion since she is not a multi-stomached animal that chews its cud like a cow or goat. Don't stand down on this...get her a second opinion. It could have been that the doc didn't see a concern after a couple of weeks, but 3 months is a long time!