I'd be more worried that my kid would not talk with me if she is under pressure at school. When a kid (like me) has to hide things from their own parent, who should be the kid's most trusted supporter and confidant, there is something seriously wrong there. In my case, I was afraid to go to my parents with my issues since they would have laughed it off or kicked my a** for being a pathetic coward!
If I were you, I'd sit down with my kid and begin becoming a friend that she can trust to share her feelings with.
I can tell we have some fundamental differences in our beliefs in child-rearing. You seem to see everything a child grows into as a direct reflection of how they are parented. I've never bought into this "blank slate" idea. If it were true, there would be one good way to parent, we'd all get the book and all raise perfect human beings. Kids are born with personalities and traits that are all their own. As a parent, the challenge is not only to figure out WHO these little creatures are but figure out what kind of environment they need to feel safe and to thrive (and it's not the same for all.)
OP, you could be the most perfect parent on the planet and your child could still hide things from you. I can't say if your child is being bullied. I can say that's it's quite common for kids to hide that from their parents and it has far more to do with how THEY feel about it then how much they trust you. They can feel like nothing can be done and that telling an adult will only make matters worse (and most schools do handle it really badly.) They can be embarrassed and not want to disappoint you (and be too inexperienced with life to understand that you wouldn't be.) I have one child who was bullied for several years and it's an incredibly complex situation to deal with. My advice is to ask your child outright. Perhaps start with your own memory of being bullied.
Then again, how old is she? It's really not unusual for young teens to pull into themselves. My DD rarely volunteered anything from 13.5-14.5. She was mopey and defensive. She wasn't getting bullied. She was dealing with other things like a bad academic environment, feeling ugly, obsessing about world problems and absorbing the negativity of the gloomy friends she had chosen during that period. It passed. My DS 13 is happier than I've seen him in years but I notice he too is starting to withdraw a bit... spending more time in his room, wanting to spend more time with friends... it's pretty normal.
I'm not saying "don't worry." I mean, you should keep an eye on things. Talk to teachers and to other adults in her life. Talk to her. However, there is the possibility that she's just withdrawing because she's a teenager.