What bridge? Once the diss is done you will be conducting a national search, correct?
In any case, telling them now leaves them with tons of time to find your replacement and should not ruffle any feathers. Is there someone else in your grad school cohort who would appreciate the opportunity?
Yes, Larry is right here (as he is so often anyway). As a former chair and, now, a dean, letting me know now is a great thing and will only cause me to be more sympathetic to your eventual application should I have a position open. I WANT my contingent faculty to finish their terminal degrees and I want to support them in whatever way I can. I really do. If I can find ways to provide financing as well as reference and other kinds of support, I am going to dig deeply. I want people teaching in my programs who really get what we're about, and, often, adjuncts working on terminal degrees really do get that. Letting your chair and dean know earlier, rather than later, and why, is a very good thing. This is not a burning bridges situation--it's a building bridges one.