Having bad boss is not your fault.  

You are correct, but bad bosses don't stay around long in good companies. 

Long story short. A friend and I started at the same time with a good company and we both had the same unqualified boss. Friend didn't want to stay. I told him to wait it out because we all knew he wouldn't last. Friend burns his bridge with the company about the boss on his way out the door. 3 months later, boss is terminated and friend wants to come back to the company and now can't get past the front door. Friend has told me repeatedly he should have listened to us and has regreted it to this day.