Anybody do this (La Conquista ... 600km Burgos to Valencia) last year, or maybe signing up for 2025?
https://laconquistabikepacking.com/
https://www.youtube.com/watch?v=BhrO_YthE38

I did the first edition in 2023, it's a decent event which follows a similar route to an annual trip I ran until last year albeit in the opposite direction. It's not as easy as the marketing makes it look especially if you're going for a 3 day completion as I was. There's some pretty technical riding early on then long sections of disused railway and lots of climbing I got the feeling that the participants are Instagram fodder with the organisers more interested in nice drone shots than focussing on things like having the checkpoints open when the riders were passing. Getting to Burgos is challenging with no local airport, I'm based in Cataluña and took the train but had to fully disassemble the bike as there was no proper bike provision on the express train. the video you linked is of the 2023 edition and you are treated to me rambling on about a place we passed which features in the spaghetti western The Good, The Bad and The Ugly. There's also a 2024 video around somewhere

Pistonbroke - Thanks for your thoughts.

I was toying with the idea of taking the Portsmouth - Bilbao ferry (no car, just the bike) and taking a couple of days to cycle to the start. Very nebulous idea to do La Conquista over 4 or 5 days (last trip I did was Tuscany Trail in 2016 (4 days) and I'm now older and more out of shape) and then spend a couple of weeks wobbling back to Bilbao mostly sleeping 'wild'.

The only bike I have is a carbon MTB (used for Tuscany) so that's a non-decision.

I have a Rab hooped bivvi and also a one man tent - I wouldn't carry both, so likely the bivvi. Cargo capacity is possibly too limited, even carrying just the bivvi (slightly smaller than tent) to take stuff for a 2 / 3 week trip, so am looking at a Tailfin rack as a possibility to enable me to take a change of shoes and clothes, stove, decent amount of food, etc..

What's Spain (rural or otherwise) like for camping or dropping the bivvi by a hedge at sunset?

Wild camping is no problem in Spain as long as you're sensible, it's strictly speaking not allowed but no-one will bat an eyelid if you follow the leave no trace rules. I can sort out a nice route from Bilbao to Burgos, allow 2-3 days as you're starting from sea level and Burgos is about 1,000 m up. You also have to cross the Cordillera Cantabria. The 9 day trip I organised up until last year finished just outside Bilbao so I know the area well. You could do worse than following my Spanish Divide back to Bilbao although it's pretty climby, there are lower level alternatives. Bear in mind that mid June can be very warm and this area of Spain is practically deserted so factor in carrying plenty of water.