Ph impedance test will be able to tell you if it's either acid or non-acidic content coming up. Helps point you in the right directions. The symptom that would be different between acid and bile is the upper abdominal pain.
I often can feel like a warm/burning liquid enter my stomach from my intestine and swoosh up to my esophagus sometimes. So signs of gastritis could be an indicator for bile reflux. I get a soapy taste in my mouth sometimes too.
If you have bile in your stomach during an endoscopy, that would be a good place to start. If it's in your stomach, it wouldn't be hard to imagine that it could reflux up.
So it kinda involves a little bit of everything to diagnose. Be warned though! Some doctors will fight you on whether or not "bile reflux" exist. I had a doctor tell me that he doesn't believe in bile reflux and that it's not possible, than I told him that apparently mayo clinic thinks it exist... Than I showed him my print outs.
Doctors don't know everything... Which is a sad because in my area, some of the GI appointments take 2 months and than you end up going to a doctor who isn't specialized enough.
That's what makes me mad... going to a guy or gal who is supposed to be "specialized" and they don't know what your talking about....