I'm afraid there is no easy answer to your problem. You drove past two traffic signs meaning 'buses only', plus text on the carriageway.
I have to say I am quite surprised they still have the rising bollard installation plus its signs, because the buses only restriction has surely removed the need for them. DO you know when these were taken out of use ? Also were you looking for the bollard when you approached ? This would take your attention away from the signs, which are much higher up.
The only other thing to note is that their sole evidence, the video, doesn't show you passing the signs. Some adjudicators will allow appeals on this basis alone.
You have one go for submmitting reps to the council, then when they inevitably refuse them, you can register an appeal at the Traffic Penalty Tribunal, but the full PCN penalty of £70 would be in play if you do that.