What you describe are definitely symptoms of coagulating protein. Not all proteins in quark are coagulated, else it wouldn't be creamy but rubbery like mozzarella (actually, more like cottage cheese, because it would still be grainy). My first guess is that the blueberry acid curdles the protein.
Blueberries are also known to act a bit strangely due to their high pectin content, I once left blueberry-banana puree in the fridge with the intention to freeze it to sorbet when I come back from work, only to find it gelled too hard to go through the machine. But I doubt that this was the culprit in your case, if anything, hydrating pectin would have bound the water and prevented the proteins from the curdling. Setting pectin would have created a mass which is firm, but not grainy, and without a separate watery phase.
As for the bitter taste, many fruits will create an unpleasant taste when exposed to dairy for a long time. Kiwis are especially bad offenders, but some melon cultivars are just as bad. I haven't noticed it in blueberries, but I don't know if I have ever mixed them. Also, there are different plants known as "blueberry", most of them just different cultivars, but the American and European variety are distinct species. It is possible that only some of them have this problem.
If you want to prevent the curdling problem, you can add stuff which will get in the way of the proteins looking for a buddy to curdle with. Fat and sugar are very good in this respect - this is why you can make lemon tarts pretty well, you don't curdle the custard despite the acid lemon juice just because the sugar content is so high. If you are trying to create a low-calorie snack, you can try gelling agents instead, which will not only reduce the curdling rate, but also sponge up the water when a bit of curdling occurs, leaving the final texture more pleasant. But it will also change the texture a lot, making it less creamier (the one creamy binding, starch, can't be used without cooking) and more like a jelly. Also you might get weird synergies between the natural pectin and the new binding agent, ending up with surprisingly firm food.
In short, the best option is to just eat it right away. Everything else has drawbacks, and is not a complete solution in the sense that it probably won't stop the curdling completely.