Free Traffic Legal Advice

There is an advance warning sign as you leave the roundabout:-
https://maps.app.goo.gl/h7wg9AE4cbXmkNtt5

The bus lane is 24x7 as the signs state "At any time".

Any particular reason for entering the bus lane, as the signs seem clear enough ?

Sorry to have to say it, but I can't see any robust appeal based on what you've said so far.

The London Local Authorities Act 2003, under which your PCN was served has a quirk related to attendance of the enforcing authority when requested by the appellant. If they don't turn up , you win as the video evidence is then void. But of course you have to risk the full PCN penalty to find out.

I suggest you submit reps on the basis that the photos on the PCN show no bus lane signs passed by your vehicle. Best to at least submit something, rather than coughing-up straight away and joining the Mugged Club

You can request their video of the alleged contravention. This is sent as a DVD and they stop the enforcement clock for about 14 days whilst they produce and send it to you.

Yea, fine, but the bus lane commences 52 metres past the roundabout and has its own signs. You could say this is too little notice,  hence they have put a warning on the roundabout. Were you approaching from Lodge Avenue ? If so, you'd likely miss the advance sign.
Bottom line is - are you prepared to forego the discount and take them to London Tribunals ? If not then it's basically game over, because >95% of representations are rejected.

Yes on the day I was approaching from Lodge avenue and took the exit - there is no sign at the bus lane apart from the white dashed line and the bus lane lettering after the Bus stop lettering.

I’m willing to forego the discount if I feel like I have a chance at winning.

Nothing is ever certain at London Tribunals, but the fact that TfL saw fit to put up and advance sign on the roundabout tells you that they recognises the very short time to react to the bus lane after one leaves the roundabout. So whilst it's not a dead cert, there is certainly a chance, plus you can request TfL attendance at the adjudication. If they don't turn up their CCTV evidence is void.