In book 1, we came to know that Dumbledore had gone to the Ministry of Magic and was gone for hours. I mean enough time not just for Quirrell to get into the hole beneath the 3 headed dog and cross the hurdles to reach the Mirror of Erised but also the trio to imitate his actions and do the same - which I am sure must have take hours for combined both. Not to mention Harry even managed to fight with Quirrell and Voldemort before Dumbledore's arrival.
Dumbledore, one of the wisest and cleverest wizard of the age, was not able to comprehend that perhaps the letter from Ministry could be a plot to get him out of Hogwarts (when he very well knows that Quirrell is trying to steal the stone - detailed in Book 7).
While meeting Harry in the hospital ward, Dumbledore told him that when he realized that Ministry hadn't called him so perhaps he was needed more at Hogwarts than Ministry.
Why couldn't he just use one of the faster ways to talk directly to Fudge?
- Travelling thorough Floo Powder
- Talking through Fire (like in Goblet of Fire)
- Apparating outside Hogwarts Grounds and so on..
Why did it take him hours to realize that letter from the Ministry was a hoax and a planned attempt to get him out of the way while the thief try to steal the stone?