I’ve got an angora so I’m also dealing with fine long hair. What you are going to need is a small, soft slicker brush, like this one https://www.amazon.com/Lil-Pals-W6202-Slicker-Brush/dp/B000O39TE6/ref=sr_1_7?s=pet-supplies&ie=UTF8&qid=1484065754&sr=1-7&keywords=slicker+brush be sure that you get one that is marked as soft, don’t buy one marked as firm or hard, that will be too rough on your buns delicate skin. You will also need a good metal tined comb like this one https://www.amazon.com/Grooming-Straight-Stainless-Collie-Poodle/dp/B01C5305MM/ref=sr_1_1?s=pet-supplies&ie=UTF8&qid=1484065905&sr=1-1-spons&keywords=metal+comb&psc=1 I prefer a comb that has both a fine and a course side.
To maintain the coat you will need to brush your bun every 1-4 days typically, start with the slicker brush, you will notice if there is a snag that there will be a bit of noise from the brush, keep brushing that area till the tangles are gone. Next go over your bun with the coarse side of the comb, if it catches anywhere youse your brush to work out the tangle, then go over them with the fine side.
I brush my bun like this every day or two, it keeps down the shedding a ton! So I’m not covered in hair and she’s not eating all that fur. If your bun is not used to being brushed work small areas at a time and give plenty of treats so they learn that grooming is good.
My girl matts very easily right behind her ears, the fur is extra fine there and almost looks greasy sometimes, I will use a tiny bit of cornstarch, that I sprinkle on that area and then brush it through/out and that helps a bunch with that problem area