Agree with the others - it sounds like fear and defending territory (cage aggression) to me. Stress also can cause bar chewing. The bar chewing might be because something isn't right for them in the cage (they can't always tell us what it is!) or as a result of changes in the cage, or too much cleaning or the scent of cleaning products, possibly, or something is causing stress. If they feel someone has been in their cage and it no longer smells familiar or things have changed, they want to escape and chewing bars is a way of trying to get out in some ways.
I also agree that taming might be the way forwards. As you say if she has a big enough cage and wheel and so on, then to me it suggests a combination of cleaning routine (apologies if this isn't the case) and a need for gentle taming to get her confident with 'the hand'. Yours in particular. They can also sense our annoyance or frustration in tone of voice and vibes given off and react against that (again apologies if that isn't the case with you).
If it helps our hamster was just like this when we got him - ferral, aggressive and it was impossible to pick him up or hold him. He chewed at the only small bars in his rotostak set up (which I later found was far too small and lacked ventilation, plus he was getting stuck in tubes). Taming was the key. Followed by a change in cage cleaning methods.
It took us almost two months to tame him (we did it in the bathtub a couple of times a week) so he was placid when being handled. And he is now meek and handleable and will even go to sleep on you. But out of the cage is very different to in the cage, which is their territory, and even now our hamster doesn't like a hand in his cage, but now he is tame he won't run at you he'll just follow the hand around anxiously wondering what it is going to mess with! It is usually much quicker than that, ours took longer because he had a cage change in the middle of it which set things back I reckon.
Change of environment can cause stress and bar chewing, and our hamster, who had not chewed bars since moved to a suitable sized cage, started chewing them after we went on holiday and left him somewhere. When he came home he was displaying signs of stress by extra activity, running round in circuits and bar chewing as if his life depended on getting out. After a couple of weeks this settled down, and took a bit of re-taming, plus setting up a playpen so he could get in and out and turning the lights off and leaving the room when he started doing it. But each situation is different really.
How long have you had your hammy? If it's not long he maybe needs to get used to you and your scent and go through some taming (which takes a bit of time and patience but can suddenly just happen as well). I found that once we were able to touch him without him leaping away or jerking his head as if threatening to bite, it was fairly instant and we could pick him up and he was fine.
Anyway - as Cypher says, if you can post a pic of your cage that might help (sometimes it is something really simple. Sometimes they are trying to tell you something (eg water bottle not working or wheel rubbing or something, or they can't access somewhere). Or give us a bit more info on how long you have had her, where her cage is and whether it has been moved to a new location recently. They are sensitive to changes in environment and rely on the scent of things as they don't see well.
Cage cleaning can be a cause of stress as well, if it is a major clean too often. I changed cage cleaning routines after watching Erin's Hamsters tips on cage cleaning and it works really well for us now. I now only do a full cage clean about once every 2 or 3 months, and even then it's only a partial clean (which means a lot of their familiar scent is left behind), and do spot cleaning in between and clean toys and wheel a different week to substrate. Having a potty litter tray really helps as well as you just clean and refill the potty every 4 or 5 days and the rest of the cage stays a lot cleaner and drier.
This is the video from Erin's Hamsters - it explains things well and has some good advice re cage cleaning
https://www.youtube.com/watch?v=5jVnEjrXbww
Defiant hamster with anger issues
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