Pulling up plants sounds like a game -- you don't seem to be saying she's eating what she pulls up? It wouldn't have anything to do with teething, this is just something she obviously enjoys. Nor does it necessarily have anything to do with being a puppy, though puppies can enjoy digging more than adult dogs. But many adult dogs LOVE digging and some cavaliers so much so that owners have to sink concrete blocks for a foot or two under the fencing line to keep their dog(s) from digging their way underneath. If you have a digger, this is not something that is easy to stop but you can work to train her to dig in an acceptable area, such as a sandbox.
The issue right now, though, is that she has learned that she rings the bell, you let her out to do what she enjoys -- digging up plants, not doing her business (BTW lots of dogs go thru this phase when being taught to ring a bell to go outside -- they start to ring it all the time to keep being let out -- the good news is, eventually that tends to lose its attraction).
She really has NO idea this is 'bad'. Indeed the fact that she runs indicates she thinks just the opposite -- that this is really, really a fun game and a great way of getting your attention. In other words, she has trained you perfectly to open the door, let her out without supervision so she can have great fun ripping out plants, then get you to fuss over her as well! It is a total win from her perspective. :lol: You have to look at what is happening not from a human point of view, but from a dog logic point of view.
So, if you dont want her doing this, then you need to stop rewarding her for all the behaviours you don't want. Ringing the bell to go out needs to only ever have the goal of wees or poops. The best way to do this is to stop letting her out on her own when she rings, and instead take her out to do her business on a lead (at her age this is a much better idea anyway-- you don;t want her to now get into the habit -- as often happens -- of going out, doing nothing, coming back in and going inside). Right now she has too much freedom to go out and do things you don't want her to do. Being on a lead completely removes her ability to tear up plants, run away, and do basically everything else besides a wee or a poop. You no longer are rewarding her unwanted behaviours.
It would also be a good idea generally to break this habit anyway -- do not let her out unsupervised where she can get access to the plants. Bring her out in the garden on a long lead for a few weeks so she can;t grab at the plants, or just stop letting her play in the garden fully for a few weeks and instead, get her out on walks. And consider setting aside an area where she is allowed to dig and take her to that area.