Hon, if you're throwing up actual bile, it means you're having some sort of pyloric sphincter problem because bile is an enzyme that goes directly into your small intestine, about six inches or so after the stomach, so there's no reason why it would be in your stomach on purpose - get to the ER.
Chances are what you think is bile might be mucus from an infection (gastritis, the flu) or stomach acid from an ulcer, things like that.
Since you have a feeding tube, get to the ER and see what's going on so they can fix you up before things get worse.
Proud mama of Mischa and Gabriel, both born post-op.