Free Traffic Legal Advice

You've blanked out too much on the PCN. You need only blank out Name and Address. We need PCN Number and car registration to see the video.
You might also care to read this: -
https://www.ftla.uk/civil-penalty-charge-notices-(councils-tfl-and-so-on)/read-this-first-before-posting-your-case!-this-section-is-for-council-tfl-dartme/

AFAIK, we've seen this location before, looking at your GSV link

is the error that I turned right, even though the bus gate is straight on? Does the bus gate include the junction?

Except that you probably drove past the bus gate sign and did virtually a U-turn, and then left turn. So you basically turned right but not early enough.

As I suspected, we've seen this one before: -
https://maps.app.goo.gl/Eepr5jKSjnq6GGgd6
As you can see there is an advance warning sign for the right-turn. However, GSV is somewhat out-of date-here so we really need to see up-to-date photos especially the bus gate signs and their position to give good advice.