It's smart that you are staying away from the bun hairpiece. I have yet to see one that does not have a comb attachment. My hair is very fine, no matter how much I move the position of the bun around I know that I will get breakage if I use those buns on my hair all the time.
Instead, I have been buying small scarves, not the large squares, but the smaller sizes -- depending on the thickness and length of your hair this should be ok --, a neckerchief size will do or go to a fabric store.
First bun your hair up and put the baggie over it. I cut strips of pantyhose and use those as rubberbands. Again, my hair is really fine, so I feel that even the Scunci seamless bands would eventually cut it because they are sealed and the pantyhose is truly seamless. Black pantyhose is also very discreet, so I would not be afraid to use it by itself if I was going someplace casual.
Fold the scarf into a triangle and then wrap the triangle around your bun. Wrap all of of the ends together neatly -- you might need to wrap the scarf ends around each other several times. Leave enough of the tails of the scarf out to tie a tiny bow.
Check to make sure that it is tight enough. During the first days that I wore this I was worried enough to discreetly tuck a bobby pin into the bow, but it has always stayed so I stopped. Again, I am always worried about breakage and I was told not to be use pins in my hair regularly, so that's another reason why I avoid the bobby pins.
Also, try to use silk scarves. This look can be really classy with the right scaf design. My dream is to use small Hermes scarves -- the reality is that I use whatever I can find on sale, LOL!