Looking at the video, you started driving into the bus lane just before the black-painted pole on the opposite side of the road. It is then easy to see this pole using GSV satellite view to work out you were in the bus lane for about 29.75 metres. You also undertook other vehicles. So on the face of it, the contravention itself seems to be made out, although I have to say it does look a bit money-grubbing of the council to serve a PCN right at the end of the buslane.
However don't just cough-up rightaway, but submit reps on the basis that you were turning left and inadvertently drove into the bus lane for a short distance so as to make the turn safely. It is quite possible there will be a camera authorisation or other technical issue. Your reps will give some time so that all these avenues can be explored by the experts on here. Provided you submit your reps so they are received