It sounds to me like you're handling things about as well as you can, but it isn't hard to foresee the need for a serious talk in the near future. Taking your account at face value, it sounds like the CNA was more or less giving you orders: "You can get the towels..." Maybe her tone was different, but I can easily believe it was just as I inferred. Aides will test new nurses (even experienced nurses new to the unit). I don't actually blame them, and I think some don't even realize they're doing it. Anyway, one way or another, they want to know whether you are someone they can trust and respect, and a very few want to see if they can get you to do your job and theirs, too.
I think you'd be well within your rights to insist that the CNA bring the linens, and promptly. I think it would be entirely right to make it clear that hanging up on you is unacceptable. I think it's essential that when you ask her to do something, it's not a request, it's an order. If you're like me, saying these sort of things will make you anxious. Thank goodness it isn't often necessary, but in my case, I've started making a point of addressing this sort of thing early on, before I really start getting angry about it. Anger is a motivator, but I'm a tad too inclined to revert to my carpentry days. (On a construction crew, "horizontal violence" can mean one or more parties ends up horizontal.)
What I use to motivate myself, what makes it necessary to do so, and how I try to frame my discussion, is that it ain't nothin' to do with titles, or egos, or anything else but the patients' care. Over time, I have come to the decision that, within my scope of practice, my patients are MY patients, and if it comes down to it, I'm the boss. If my charge nurse doesn't like it, he or she can relieve me of my assignment. If my manager doesn't like it, she can fire me. If my assistant or a fellow nurse doesn't like it, tough. As long as a patient is assigned to me, I call the shots. But I also try very hard to include the assistant, to make it OUR patient. I know what I respect in a doctor, so I try to project those qualities as a nurse. But I often tell my patients, and practice as a nurse, what I learned when I was a patient: It's nice to be nice, but it's important to be heard. If you have to chose one or the other, be heard. (Then I work my butt off not to make them chose.) Good luck.