Let's put aside the question of how a huge snake could fit into the Hogwarts water pipes (they're magical pipes!) and exit them at random points (there are magical pipes/walls with built in portals only a basilisk can open!) to attack isolated Muggleborns (how would a snake know the difference?) unfortunate enough to be isolated (they really should've known better!)
My question is: How is it possible for a 60 ft long snake not to been seen by anyone/anything (for a giant snake it sure was a master of hit and run)? Even though there are hundreds of portraits everywhere through the castle, at least a hundred of house elves working all over the castle, and at least 20 ghosts roaming around (according to Ch7 of PS). Even if direct eye contact is necessary for a true kill and indirect eye contact (i.e. reflections) results in petrification, how is it possible that not a single soul saw it while it was retreating to the pipes? Not a single portrait/elf/ghost told Dumbledore "Hey headmaster I just saw a 30 ft long scaly something disappearing through wall/to a nearest bathroom, but I didn't see its face."