I timed this to be 11-12 seconds. The OG Way

I timed this to be 3-5 seconds. The way to do this skip using Story Mode characters (The Riddler and Mr. Freeze)

I timed this to be 2-3 seconds. The same as the previous way, but you jump on the door handle instead of the fence. i.e. the fastest way to do this skip in Story Mode.

Original skip credit to @Zed for finding the way to do this skip in Free Play.

His Video: