You see, but to make this work you have to go through very strange steps of logic that really don't make sense.
The big one is: how rare is gunpowder? Well, all gunpowder is, is a mix of charcoal (which you get from trees), sulfur (necessary for plate movement on a planet, and just generally common), and a type of salt. The process to make it might be unknown for most people, but gunpowder doesn't make sense unless we go through very strange environmental loops just to fit a square peg in a round hole.
And it gets even more unlikely when you realize that gunpowder isn't actually necessary for guns. Now, it's one of the best for using guns (and rockets) because of how cheap and easy to make it is. But military grade guns have been made with: compressed air, alcohol, and steam. Hell, in theory any small scale explosive should work, there's just no real reason to try because there should always be enough gunpowder around.
To get the setting to work that like that you have to get into strange things like: burning trees in this universe doesn't create charcoal! Which goes so far outside the realm of what (I believe, if a Rioter wants to step in and correct me, go ahead) any author actually did when making and designing the setting. And that just opens up more questions: Charcoal is a natural occurrence from pressure, heat, and wood. How different would the wood have to be to not turn into charcoal? Would it even be possible to use a charcoal-less wood as fire at that point? I honestly, have no idea, but tampering with chemical compounds leads to very weird rabbit holes. The same is true for sulfur and saltpeter, they really just happen in abundance.
You also wouldn't really have to trade for bullets, unless you're specifically thinking of actual modern guns. Medieval to Napoleonic bullets were just small round bits of metal. Lead, usually, because it's plentiful, and easy to shape. Soldiers made more bullets on their own, melting down soft metals into a very small mold. This stuff should not be hard to come by.
As to the spread of the technology itself. I think you're a little behind on the lore here: Demacia uses mages but they're supposed to be incredibly rare. Magic in general was supposed to be incredibly rare outside of Ionia and places like Ancient Targon and Shurima. I can sort of understand modern Freljord not having guns: they have apparently a rich history of longbow use, and the Britains were late to the whole gun thing. That and they're barbarians off in some corner of the world. (Though funny thing, in the Pantheon short story, the raiders are described like Freljordians and one of them is carrying a gun, but that could be just a strange happenstance). But Targon itself? Which is supposed to be some sort of Mecca, and constantly attacked, should totally have gotten guns by now. Demacia and Noxus, also I'd say definitely.
Interestingly, Demacia has kind of amazing tech, just look at Jarvan's armor. Ignoring the fact it's impractical as all hell, that is a high end articulated plate piece. That stuff wasn't around until around the 16th century. Doing that actually takes more mechanical knowledge than creating early guns (and to get really funny, the metal processing used to make them required charcoal). And even more interesting, it's currently theorized that this type of armor only even came about because of the rise of mass cheap guns causing the escalation in armor development.
This is what I mean by jumping through hoops upon hoops of logic. Is it possible to come up with some sort of very specific set of circumstances that answer every single chemical, historical, environmental, technological, and social question in order to make the setting fit? Yeah, probably. Do I think the authors did? No. Would it just be easier for all involved to just go "Yeah, these details don't bother me, and I like the setting, I'm just going to roll with it"? Yes.