What a pain in the ass.
First thing i'd do (and i know it sounds silly) is check all the facts on the notices to be correct and also check the times of operation of the bus lane. You'd be suprised how mant are just signposted wrongly.
If those are ok i'd attempt an appeal, tho you have no leg to stand on, but at the end of the day you have nothing to loose either.
Maybe along the lines of "i was only filtering past that one car, sur;ey if a car had two wheels over the line into a bus lane he wouldnt get a ticket as he is not using the lane at all, just happens to be over the line.
You'd really have to sell that well, cos they could have you on video passing 20 cars or so, or it could be a static camera.
I got done once in a bus lane and they sent me 2 pics of me doing it. In a car that was though... so i sent em a cheque.
Where i live NW london they have the trial on for bikes in the bus lane, if you offence wa anywhere near one of those "trial lanes" then use that as a justification maybe.
Worst comes to the worst pay em and get em off your back and be gratefull they dont give points for bus lane offences.
Loads of balls imo, this whole "trial". If its safe enough for pedal bikes to be overtaken by buses then its safe enough for motorbikes to use the bus lane.
Good luck anyway