Are there any steps I should be taking at the moment?
Yes ! Keep your eye on the calendar, because you only have limited time in which to submit representations.
A quick look at GSV shows there is an advance warning sign of the bus lane here:-
https://maps.app.goo.gl/orgbGSU3kqtKKATf8Question is, of course, is the sign still obscured ? The sign is highly visible in this GSV 2021 view: -
https://maps.app.goo.gl/cwnWNftC8krHKaZd8Then along come the usual thick and stupid council parks department on 2022 to plant trees to make it all look pretty: -
https://maps.app.goo.gl/8j3QywnYo4LXVUpE8and the trees flourish !
In addition, the sign is placed well to the left and not in a driver's line of sight.
However, having just passed your test, you need to get very rapidly up-to-speed on bus lanes in London and their signs.
I was unsure if the road markings meant it could enter the bus lane as the line was broken at the entry.
This road marking is the standard taper marking for a bus lane about to start. The blue sign just beyond it is the start of the actual bus lane.
Finally, your narrative doesn't match what I see on their video. It shows you driving from the traffic lane into the bus lane, past the sign and the traffic island, then the motorcyclist comes past in the traffic lane, and you re-enter the traffic line a short distance after the bus lane starts.
So what does the above mean ? Well, it means you should submit representations on the obscured advance sign, and that the bus lane appeared as a complete surprise to you, (the video shows you slowing down), and due to the traffic island you were unable to avoid it so had to continue into it before leaving directly the traffic island was passed. This could be a win at London Tribunals on the signage. It might be useful to see if the statutory register at London Tribunals have any cases here.
https://www.londontribunals.gov.uk/about/registers-appeals
