I am not out as trans at work (I identify as lesbian at work) because it will be almost three years before I am permanent on my job. My therapist, knowing I was distressed that I would have to wait three more years before I can even start to transition, suggested I have top surgery first. Her thinking was that the is not unheard of for a woman to have a mastectomy. Then I could start T once I was permanent. I was wondering if anyone else out there had gone this route. I am concerned about losing my job because I present so not cis gendered.
This sort of depends on your situation. I have an a-cup, and I wear tight exercise bras everywhere. If I got them chopped off the general public wouldn't notice. For you I would be more concerned about explaining the reason why you have to take so much time off of work to get the surgery. I also wonder whether it's better to take hormones or get top surgery first. Hormones cost less and are easier to reverse in the short term...
Some guidelines say that you have to have lived "full time" for at least a year in order to have surgery. That would likely be one of your biggest obstacle. There are surgeons that will do top surgery without T. I'm not familiar with explaining taking time off from work, but mastectomies are in no way trans exclusive and it's possible that it won't arouse too much suspicion. Some people get them in order to prevent breast cancer (though this usually only happens when there is a very strong family history of it), but the people that need to know about why you're taking time off aren't going to go dig into your family history (and I'm quite sure that it is illegal to require you provide such information). Some states have legal protections for trans people so that they can't get fired from their jobs because they're trans. You might want to research the laws concerning this for your state/city. There's still the chance you'll get into some sticky situations even if those laws are there, but at least you know the law is on your side.