I'm not very well versed with guns, but I know my way around magic systems. As far as I can see, you can probably tweak damn near any kind of magic into working with guns.
First off there's the one you already implied, the magical ammo thing. You could have normal bullets imbued with magical elements (fiery explosive rounds, freezing rounds, etc), or just straight up magically created magic ammo. Depending on how you choose to do this basic thing, it'll probably have some heavy implications for how non-elemental magic can be applied to bullets.
Starting with normal bullets and adding magic to them would turn it into an enchanting sort of thing, so for starters you could do pretty much anything that would make sense to throw on a sword as enchantment. Bullets that suck the life out of targets to heal the shooter, bullets that suck the soul out of a target and maybe store it in some vessel (totally thinking of Elder Scrolls soul gems here), bullets that make no sound at all, bullets that cause the target to be stunned/paralyzed/silenced, bullets that impede the target from using their own magic (mainly useful if the bullet enchantment thing is done on the fly rather than requiring users to enchant their ammo before heading into a fight because it takes some time/effort/materials), etc. To have this sort of system make sense it would probably require gun magic to be heavily focused on offense, because you're taking bullets, which are inherently offensive and meant to cause damage, and just adding effects onto them. Your magical blades thing could fit in here by having a bullet that interacts with the target like a normal bullet because its spell effect is just to make magical constructs attached to the guns. This could also work to make magic shields that activate upon firing, giving the gun mage some defensive cover from retaliatory fire. You could also probably get away with these bullets giving various positive effects to the shooter, like greater speed/strength or temporary invisibility, but it wouldn't make a ton of sense to allow these to confer beneficial effects onto allies or do things in a large area around the shooter because to maintain consistency it ought to all be based on physical contact with the gun(s) that fire the enchanted bullet(s).
However, if instead bullets are conjured entirely by magic, you can get away with a lot of other stuff because they can be entirely non-physical entities. This sort of system could remain logical while making use of any kind of spell that could feasibly be fired as a projectile, because this system would basically be using guns as a focus to fire spells in the same way as some magic systems require a wand or staff to do magic. For this one you could also go either way on using magic off the cuff or requiring users to pre-make their spell bullets, with the latter being better if you want to force players to have limitations and need to be strategic about how they use their resources. On top of all the uses listed above, these kind of bullets could do things like heal targets (because it's just a healing spell shaped like a bullet), cast big area of effect beneficial spells centered on the shooter or the bullet impact site, create a shield in some shape around the impact site, cause a target to become invisible, cause a target to become immune to mundane or magical damage, create remote or proximity detonation spells of all kinds (various elemental stuff, magical bindings, silent alarms to watch for intruders, etc), make a runic spell spread out around the bullet impact site and do all sorts of nonsense, create a magical rope that goes from the gun and gets anchored into whatever the bullet hits, open up a telepathic communication channel between shooter and target, do some mind reading nonsense to the target, cause a mind control effect, and so on. Basically anything you can imagine being shot out of a wand or staff in some other magic system could be worked into a bullet shaped package for this system.
Aside from magic bullets, you could do the magic blades thing in a very different way. If you treat guns as a magical focus in a general way then you could get all sorts of nonsensical with them. Essentially you could say guns in your world are equal to wands/staff/magic words/whatever in other worlds with magic systems. You'd probably have to do some worldbuilding to explain why the hell that is the case, but it would mean anyone with a gun (or anyone with a special magical gun, whatever) can do any kind of magic without needing to rely on the bullet thing. Instead of needing a bullet enchanted with a spell that basically says "make a magical blade pop out under the barrel when fired," you could just have you gun mage will the magic blades into being with their magical power. Instead of actually firing a bullet enchanted with explosive power, they could just point their gun at a target and cast an explosion spell with their mind. Using this kind of shenanigans would mean that you'd essentially just build an entire magic system from the ground up (which you'll probably want to do regardless, just to make sure all your magic stuff is consistent, and if you need any guidance on that there are some relevant threads to be found in the Worldbuilding Guild and its Expansions subsection) and decide that these guns are the magical foci required to do any magic. If you were to do this, I'd say it would make the most sense to use the magically created bullets thing and have those be used as spells prepared in advance with no magical energy drain on the gun mage, whereas doing those on the fly spells would drain their reserves. That would make for a nice balance between prepared resources and mana management, I think.
Alternatively, you could stick to gun magic being completely bullet based and also have other kinds of magic in the world. If you go with this route, then you ought to give gun magic some pros and cons compared to other kinds of magic to explain why some would choose to use guns while others stick with other methods. For example, perhaps gun magic has the perks of being covert (a handgun is easy to carry secretly) and the guns can be used as a mundane weapon if needed and it's less strenuous to use in combat because you have to prepare your spell bullets ahead of time so all the magical energy expenditure happens before the fight, but it's limited because you're stuck with whatever magic ammo you brought with you since you can't make new things on the fly. For contrast, magic done with a staff could be extremely versatile because you're doing your spells on the fly and possibly significantly stronger in the magical effects you can achieve (say an explosive bullet could blow up stuff in a radius of a few feet but a determined staff mage willing to blow all their energy in one go could level a city block with one spell), but it's hard to be stealthy because it's hard to conceal a big gnarled staff and it's physically/mentally taxing because you're having to expend that magic energy to do it. If you go with this idea, then you should build the magic system as normal and just separate the methods of directing magic after you've laid the foundations for how it works on a fundamental level. The source of magic power (gods, inner magic reservoir, etc) and method of gathering that power (some special ritual, concentrating a certain way, etc) ought to be the same across all casting methods, but how that magic is directed and what effects may be achieved could differ a lot if you want it to.
That ought to give you plenty of ideas and things to think on. :P
