emi, I think you probably have to deal with each situation as it arises. Some people may be genuinely interested, not condescending, not shocked, but lacking in knowledge. In that case, I would certainly talk with them frankly and helpfully, giving them a guide on where they can find out more, too, if they are interested.
I get the feeling that you are a little scared that people are going to bother you - or your Master - in a predjudiced and leering way. Them, you have to try not to let them wind you up. It is like any other predjudice. I would personally try to avoid any discussion with them; if obliged to, I would be polite if I could.
It is because of this sort of predjudice, and also in order to respect others who would be disturbed or shocked and upset by the concept of a D/s or BDSM relationship, that I also think it is a good idea to be subtle. You are not in the relationship, you are not wearing your collar, for the shock factor: you are doing it because it is part of your loving life. A collar for outdoors does not need to be any more noticeable than a wedding ring, to others. But you both know about it, and it means the right thing to you.