If you've suddenly started waking up with a Vomit Taste in your mouth then it's likely you have either a bile leak in your body or you're just suddenly starting to suffer from Acid Reflux disease.
Acid Reflux disease is caused by the stomach acids flowing into your esophagus, while bile reflux is caused by the bile fluid from the small intestine flowing into the stomach and esophagus.
It would be best to get checked out by a doctor for either the bile reflux or acid reflux especially if you continue to wake up with a Vomit Taste in your mouth.