Thanks for the additional information. I really appreciate it.
Since you're seeing yellow bile every morning, I suspect she may be suffering from the doggy version of acid reflux.
Just like in humans, if a dog builds up too much stomach acid from not eating for several hours (which is why she only does it in the morning) they can have some vomiting. Some owners opt to feed a small meal in the middle of the night, through the use of a automatic feeder, but since you feed human grade food, I don't know if that would be feasible for you, so you may want to look into an over-the-counter medication to help control the acid.
When it comes to treating acid reflux, I've found the use of Omeprazole (Prilosec) seems to work a bit better than the Cimetidine (Tagamet). And although I'm sure you'd prefer not to have her on a medication for the rest of her life, the Tagamet has been used in veterinary medicine for many years as it has been incredibly safe to use for years on end.
You can find more information here:
You could also try adding some boiled white rice to her diet in the evening meal to see if that is a little easier on her stomach and could provide a starchy barrier to help keep the acid down a bit longer.
I hope this helps.