You are going at a very crowded time. There sould be ZERO problem meeting ppl. Hang out the Belvedere for drinks, you will meet ppl there. Also, go to the Tropicana Bar at Paradise beach during the day, N'ammos on Psarou beach during the day (both places kick up after 3pm), Caprice in Little Venice for sunset. At night there is a good crowd at Astra, Caprice, Bar Uno, Celebrities, and if all else fails...Skandanavian Bar (drinks are cheap here and they have a disco upstairs). You will then meet plenty of ppl and can go to El Pecado (club) after 2am and to Space (club). The clubs in Mykonos do not get going until around 2 or later. There is always after-hours at the Yacht Club in town by the port or at Cavo Paradiso.
You will really have NO problem meeting anyone. Too bad you weren't going in August, I have an international group of singles (and some of are not) that will be there mid-end of August!