Here are some random thoughts..
I think it matters if the taste is constant vs. rare/intermittent. This is based on the assumption that bile is not going to reflux all by itself, it is the gastric juice that refluxes which contains bile. But it will also contain acid, pepsin and other stuff I'm unaware of. So if the taste is constant, and if the person is tasting the reflux itself, that means your entire esophagus and throat is subject to acid reflux constantly.. which means you would probably have horrible throat pain, be unable to speak, teeth rotting, the whole nine yards. True, the reflux becomes less acidic as it travels proximally since it's being buffered by saliva which has pH around 7.
If the taste is intermittent, it could be the way someone's body responds to reflux. This could be established using 24 hour ph/impedance study. In my case, it was very highly related to weakly acidic reflux during the ph study, however, my taste is constant and not intermittent. I had ~55 weakly acidic refluxes if I remember right, but that is not enough refluxes to have 24 hour sour taste.
I've not seen it written anywhere, but I think the sour taste could be the body's strategy to try to encourage swallowing in response to reflux, i.e. by generating a foul tasting substance in the mouth. A throat tightening (globus) sensation I think can also be a response the body uses to encourage swallowing. Swallowing saliva, or even dry swallow, can help to push down whatever the body feels to be refluxing.
There are several papers by Ronnie Fass MD, dealing with refractory GERD, where he recommends tricyclic treatment for people who have a sour taste -- they are termed hypersensitive esophagus. However as far as I have seen, he has given no explanation for this in these papers. It is unfortunate that there is lack of clarity with respect to various sour tastes, or even what "sour" means. I have had acid taste in my mouth, which burned my throat, and I could classify as "sour". But I also have a constant taste which classifies as "sour". So in both cases, I could describe it as a sour taste, but one I really believe to be acid, and the other, something else.
As for something else. I think it's about 40-60% of people with burning mouth syndrome (believed to be a neurological condition) often have sour/bitter/metallic taste. In the literature it's called dysgeusia, which means "distortion of the sense of taste"-- but I don't think that term fits perfectly, because many BMS patients have no such taste when eating. So if they actually had 'dysgeusia', their sense of taste of food would be distorted. But that aside, a sour taste can have nothing to do with any sort of reflux, it can be a neurological phenomenon.
I tried a test once, feel free to give it a go. When I had a strong sour taste in my mouth, I spit a good amount into a spoon. I then had some water, cleared my palate, which temporarily relieves my sour taste. I then tasted the spit in the spoon. It had no taste, just boring old saliva. Whatever was sour was not in the saliva, as seemed to be my experience of it. In fact, that might be a good way to tell whether there is reflux in the saliva or whether the sour taste is coming from some neurological experience. If you try it please let us know. :)