Yes, when my dog of the same age started vomiting bile, it was because his pancreas was failing. Time to get some basic labs done at your vet and look at basic organ function like pancreas, liver and kidneys. If caught early enough, the damage can be minimized and symptoms managed for quite some time unless the underlying cause is something like cancer. In older dogs, it's usually just a case of old age and organs not able to function as well. The trick is to diagnose early and make diet and medication changes to prevent worse damage.
She is probably hungry, does she have a bowl of food or only fed certain times of the day? Our older dog will spit up a yellow coloured bile when she hasn't eaten in the morning yet. Feed her a little earlier or give her a few treats till she gets her food, if that doesn't solve the problem definitely do take her to the vet to be checked out.
Thanks for your suggestions!