That's not perfectly accurate, and that doesn't answer the question in the thread.
For a character to jump, they must first squat on the ground (which is easiest to notice with Bowser). Each character's shorthop takes a specific amount of frames of jumpsquatting, with frames being the rate at which the video plays. 1 frame is 1/60th of a second ; 4 frames is 4/60ths [1/15th] of a second ; 60 frames is 60/60ths of a second [1 second]; etc.
Fox is -tied- for the fastest jump (shortest jumpsquat) with 6 other characters at "3 frames squatting on the ground."
Bowser, however, is indeed the last and alone in that jumpsquat period, with 8 frames squatted on the ground.
Full Jumpsquat durations in frames: (The above poster's list was somewhat inaccurate)
3 frames [airborne on frame 4] – Fox / Ice Climbers / Kirby / Pichu / Pikachu / Samus / Sheik
4 frames [airborne on frame 5] – Captain Falcon / Dr. Mario / Luigi / Mario / Marth / Mr. Game & Watch / Ness / Young Link
5 frames [airborne on frame 6] – DK / Falco / Jigglypuff / Mewtwo / Peach / Roy / Yoshi
6 frames [airborne on frame 7] – Ganondorf / Link / Zelda
8 frames [airborne on frame 9] – Bowser
The question in the OP was how long someone can hold the jump button and still shorthop, and that was answered earlier in the thread.
To shorthop, you only have to let go of jump before the final jumpsquat frame. In other words, if a character is on the ground for 3 frames like Fox or Sheik, then you have to let go of the jump input either on the first or the second frame.
As such..
Shorthop input windows (Let-go-of-jump-within..):
2-frame shorthop input windows – Fox / Ice Climbers / Kirby / Pichu / Pikachu / Samus / Sheik
3-frame shorthop input windows – Captain Falcon / Dr. Mario / Luigi / Mario / Marth / Mr. Game & Watch / Ness / Young Link
4-frame shorthop input windows – Donkey Kong / Falco / Jigglypuff / Mewtwo / Peach / Roy / Yoshi
5-frame shorthop input windows – Ganondorf / Link / Zelda
7-frame shorthop input windows – Bowser
I know you might already understand this fully, but if the thread is going to get locked, then this concise post should be present for people to work with.