dumbledore never flew on a broom

“We need to return to the castle at once,” said Dumbledore.
“Rosmerta” — and though he staggered a little, he seemed wholly
in command of the situation — “we need transport — brooms —”

“I’ve got a couple behind the bar,” she said, looking very frightened.
“Shall I run and fetch — ?”

“No, Harry can do it.”

Harry raised his wand at once.

“Accio Rosmerta’s Brooms!”

A second later they heard a loud bang as the front door of the
pub burst open; two brooms had shot out into the street and were
racing each other to Harry’s side, where they stopped dead, quivering
slightly at waist height.

“Rosmerta, please send a message to the Ministry,” said Dumbledore,
as he mounted the broom nearest him. “It might be that
nobody within Hogwarts has yet realized anything is wrong. . . .
Harry, put on your Invisibility Cloak.”

Harry pulled his Cloak out of his pocket and threw it over himself
before mounting his broom: Madam Rosmerta was already
tottering back toward her pub as Harry and Dumbledore kicked
off from the ground and rose up into the air. As they sped toward
the castle, Harry glanced sideways at Dumbledore, ready to grab
him should he fall, but the sight of the Dark Mark seemed to have
acted upon Dumbledore like a stimulant: He was bent low over
his broom, his eyes fixed upon the Mark, his long silver hair and
beard flying behind him on the night air. And Harry too looked
ahead at the skull, and fear swelled inside him like a venomous
bubble, compressing his lungs, driving all other discomfort from
his mind. . . .