I would be really shocked if you were pulling out new fur… How was she reacting? Did she seem like she was in pain when you yanked that out or just a little annoyed? Also, what did those mats feel like? Were they hard/soft? Big/small?
When buns go through their heavy molt (I’m not sure where you are but a lot of us are dealing with that right now) there can be spots where you are “plucking” (pulling out those loosened tufts of hair that stick out) and if the shedding is really condensed in that area, you could pull a lot of fur out that and make your bun very close to being bald without hurting the bun. Once, I did this to my bun’s head. She looked really goofy for a while with the new fur being just a very short area of black fuzz.
If she is getting mats on her bum that are actual true mats (the fur stays clumped together after you pull it out) and it is mostly around her bum, you might need to consider that her littler box is staying a little dirtier than it should be. What kind of litter are you using? Simply switching to a more absorbent litter or one with less dust could help with this.
As for grooming, I have tried a lot of things and I have to say that the hairbuster comb (I bought mine on the binkybunny store) is the BEST tool. It pulls the undercoat out much more effectively than any cat shedding comb I have used. I have a grooming glove as well. It does not really help on the rabbit but it is great for getting all that fur off the couch!
🙂 Hope some of this helps!