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Ooooh, it looks ok, thanks for the link h20.
I'll probably be travelling back off-peak, depends on my little legs and post ride munchies and thirst quenchisations.
FatManOnAFixie-
You'll be fine off-peak. In a 4 coach train the bike section will be either in the 2nd or 3rd (more commonly 3rd) coach. If it's the white rolling stock the door to the bike bit has two blue triangular flashes above it. If it's the newer blue rolling stock, the door to the bike bit has a red band down the side of it. I'm pretty sure Southeasterns booking system doesn't allow you book a bike rezzie.
I've never had an issue with getting bike onto one of their trains - it's a journey I do regularly. If the bike section is full when you get on, put your bike in the doorway opposite to the one you used to board. The doors on that side won't open until the train gets to Bromley South - by which time you will be gone.
JurekB
Check with the operator. Generally yes, but there are sometimes limited slots and operators are increasingly fussy about bikes being transported without using a dedicated slot. If in doubt, reserve a slot - usually it's no additional cost if you have a seat reservation.
Edit to add - here's southeastern's bike policy. Off peak you seem to be okay.
https://www.southeasternrailway.co.uk/about-us/policies/bike-policy/