Yes, you are using it perfectly.
It is an old word that we do not use very much. It is still used, at least in Australia, but mainly in product advertising (e.g. for beer or electrolyte drinks) or for a very emphatic expression indicating that the thirst is or will be completely gone (like the other usage of the word, meaning to extinguish a fire completely).
Some other examples would be:
(Product X) quenches your thirst, fast
Quench that thirst (with Product X)
Wow, that drink really quenched my thirst! (this is a bit weird and not really something that I would say except maybe ironically in a pub). In general conversation with native-speaking friends, I would probably say something like "I am really thirsty" or I was really thirsty until I drank that", avoiding the use of the word.
It is not incorrect to use it and we do use it, but it is a bit formal and old-fashioned. It is more likely to be used between educated people and in product advertising that suggests that the associated drink is very good at fixing your thirst.
I hope that this is helpful. It is an interesting word.
EDIT: I think that part of it is that I would rarely talk about the need to get rid of thirst! The word is perfectly ok, it is just not something that you use very often. Maybe it is because I don't talk about thirst very much. ;)
EDIT 2: Andrew Goddard's comment above is also correct, I did not see the question in the heading "When I bought a bottle of water, my thirst had already been quenched". I don't think that this sentence is grammatically incorrect but it is a bit unusual. Why would you buy water when your thirst had already been quenched? It is a bit like saying : "I was already full when I ordered the meal". It is a possible situation but it is unlikely to occur.