Vomiting bile in the morning

Don't mistake true vomiting with acid reflux spit ups. Our Boston has acid reflux and quite often after running hard, jumping off the bed, getting overheated, or just for no reason, up will come yellow foam, or,white foam, water, and even occasionally a piece of kibble. It just seems to spill out of her. Sometimes we give her an acid reducer for a few days and she gets a break from it for awhile. She feels fine, digestion is good, it's just that she has gerd, just like people. It took us a couple of years to figure out what she ate had no effect, just when and how much. We paid astronomical vet bills trying to figure out why she was "vomiting". Vomiting is stomach spasms and foul vomit...we only saw this once when she was truly ill. She rarely vomits, we call it throwing up.