How did Dumbledore discover the Room of Requirement? (SPOILER)?

Ok, just for fun: Dumbledore tells Karkaroff in Goblet of Fire that he found a room full of chamber pots (or something like that) when he was in great need of a bathroom. Harry later umes that Dumbledore was refering to what he later finds out to be the Room of Requirement. But the Room only opens if we p 3 times in front of the hidden door, thinking of what we need. Why would Dumbledore walk backwards and forwards on the corridor and not go straight for the nearest bathroom he knew of? This makes the Room pretty hard to find by accident. Nevertheless, and although Dumbledore didn't seem to know about it, a lot of people seem to find it, judging by Trelawney and the piles of rubbish and hidden objects in there (which makes me wonder how Voldemort could possibly hide his Horcrux there, in the middle of the garbage, and think no one would get near it). What do you think?