Your Glock 20 is a 10mm semi-auto, with a 4.3" barrel, correct (I just Googled it, no prior knowledge). If so, then you are OK to use it---the point is the handgun must have a barrel at least 4" in length.
I am in Kitsap, but have no knowledge of those two areas. Yes, there are black bears here (a lot), and yes, a hunter in the public areas can be successful. I have no specific advice for you, except to state the obvious. Strap on your boots, and get out there. Green Mountain in particular will have a lot of hikers and mountain bikers, so you will have to explore, and get away from the crowds. The blackberries are just now starting to molder, and will be gone in a few weeks. Get out now, right now.
In general, find areas of blackberries, away from crowds. If you find bear scat in the area, set up above the berry patch (on higher ground, I don't mean in a tree), and stay there. Bears can be hard to spot sometimes, so look for movement in the berry patch. Know your target! Do not just shoot into the patch!
And have fun.