The answer to this question will vary depending on where on the spectrum you are and I am answering based on my experiences with my brother and a friend (who both have Aspergers).
The fact that you are a programmer may work slightly in your favour as in many places there is a stereotype for people in that line of work to be socially awkard. There is also growing awareness of aspergers and the behaviors associated with it in many countries so it may be that it is not just your supervisor who has suspected it. (If this causes anyone to judge you negatively it is their problem, not yours.)
In terms of negating perceptions that you are being rude there are a few approaches you can take. The most obvious being that if someone says that they are offended you can hopefully explain that it was not your intention. If you are not sure if something you have said has offended someone (I know it can be hard to tell sometimes) then you can always say "sorry if that sounded rude" or "maybe I didn't word that as well as I could have", just in case.
In terms of being forgetful I am not sure what you feel you could have done to give this impression but it could be a good idea to keep a logbook of your work and what is requested of you and also to keep any emails that may be relevant at a later date. If it's for less work related things like people's names or other personal information then there are techniques that you can learn to help with these sorts of things.