Here is how I approached a similar situation in the past.
1. I continued to do my job as best as I could.
2. I aggressively looked for a new job that I would enjoy and be able to contribute.
3. Only after I had accepted another job did I resign.
4. When I resigned, I did it professionally and strived to leave them in the best shape I could.
5. This didn't happen, but if I was sincerely asked why I was leaving, I would have tried to professionally share the things I thought could make a difference. I wasn't asked, so I didn't provide the feedback.
Burning bridges is never a good thing. I've been literally stabbed in the back before by bosses that lied to my face. I did not burn the bridges... I just became educated about the level of trust I could extend to them and I made sure I didn't get myself into a situation where they could hurt me.... and in some cases I warned my peers that I had a high level of trust with. If you burn a bridge, you never know when it will come back to bite you.
As an example, I had an employee quit on me at a very bad time. I was quite furious with how he did it, and his lack of doing a reasonable turn over before going out the door. I didn't blow my stack and say things I'd regret, but he knew I was furious. Six months later I called him up and got together with him for lunch. I told him how I felt when he left, and I also told him that I understood why he left, and finally I told him that I didn't want our relationship to end on that note and that I wanted to put it behind us and move on. I wished him well in his new job... something I couldn't do when he left. Fast forward a number of years and he had changed jobs a few times and was a Vice President at a tech company. I was changing jobs and needed a good reference, and he came through for me.
You never know when and where your network of contacts will show up or be called upon.