first off, you are a bonehead for not putting anything in your airlock
second, water isn't the best for airlocks. some star san/iodophor solution, or a 40% alcohol spirit (cheap vodka, gin, brandy, whatever) is what you should use.
DO NOT throw out this batch. continue bottling. there is a chance that you picked up an infection, but i'd say it's a pretty small chance. even if the airlock was empty, at least the carboy was physically protected from the outside nasties: bacteria and whatnot can't travel on their own, they need to hitch a ride on dust or some other airborne particle. so unless the airlock itself was contaminated, chances are good you'll be fine. once fermentation started, your brew produced CO2 and that helped push things out. once fermentation was done, you had alcohol in there that also helped control infection.
so go for it, and be sure to open your first bottle carefully in case you get a gusher. taste cautiously... then enjoy!
