I can't offer much sage advice because I really wimped out on telling people. It sounds like you are in a bit of a different situation, though, or at least I hope that you are. We had concerns with competitiveness, jealousy, and I guess some of the same worries about sounding like braggarts.
I wound up not telling virtually anyone and waiting for it to be found out via the grapevine, which is what it sounds like you are trying to avoid probably rightly so. The only people I had to tell were family members who were less than supportive as well and I was almost apologetic in telling them.
The only thing I can say that we did that probably made it sound less "braggy," when we started getting questions from others when it came out via grapevine was to say that we were approached by the school who felt that placing her in the next grade up would be a better fit. That was honest and it also seemed to go over better than suggesting that we felt that she was so advanced that she needed to be skipped. I tried to be short, simple, and not expand unless pressed.
I did get some questions about how we got her skipped, what types of information they needed, etc. and I probably didn't handle those as well.
