It is purely speculation to think on it, because they don't explain how she manages to do it beyond that she learned it, but I've given the idea of how limit breaks work, and Quistis's in particular, a good deal of thought myself.

My theory's a bit similar. Para-magic usually requires some sort of power source, like the GF, to function properly--I'm going to assume that, for the magical limit breaks, this power source is the status that makes the limit break happen--adrenaline, 'spirit energy', whatever you want to call it--or an Aura spell.

...And then blue magic is just another form of para-magic, based on monsters, rather than on Sorceress magic. The difference, though, is that blue magic is very rigid in what it can do and how it is used--you need the item to make the ritual to learn the 'magic', more or less, and also, unlike the other limit breaks, Quistis's blue magic isn't affected by how much 'danger' you're in. Where you get more time on Duel if you're at lower HP, or better spells for Selphie (whose limit break is just weird, but fun), Blue Magic is Blue Magic, no matter when you cast it.

...And, if you ask me, she did the research and taught it to herself (though she didn't create it, of course), maybe while she was at Galbadia Garden, maybe not, but mostly because she didn't have much natural magical talent and that's just the kind of person she is.