I’ve only raced the previous version to the previous version (known as the Western Isles Challenge back then), but have a fair amount of experience of similar events. As Pyro says, a backpack would be preferable to a bumbag given how much you’ve got to carry – I doubt you’ll see many with bumbags. Just take a small backpack. Definitely have some sort of bag on the bike (I’ve always had a seatpack) to put in bike specific stuff so you don’t have to carry it on the run – though I’d always carry running shoes in my backpack, it’s handy to have external elastics so you can just shove them in and get them out quickly without opening the main pack.
My preference is normally to use bike shoes on the bike and change to running shoes for the foot sections – doesn’t take very long to change and the running shoes won’t weigh you down that much when biking. That’s for longish legs without many changes which I presume is what you have. For shorter legs and more changes I have worn running shoes on the bike and it can work OK – if you’re doing that I recommend Powerstraps or something similar rather than flats (which most running shoes don’t work well with) or traditional toe clips.
Regarding bike choice, do you not have any sections on the machair (the bit bordering the beach on the West coast)? I’d not want a CX bike there, fat bike territory, though decently wide tyres on a 29er should be good. TBH there’s not a huge advantage to a CX bike on road sections if you know what you’re doing and can get an aero position on your MTB – I’ve fitted tri bars to my MTB before now for road sections (when I raced out there I had 2 bikes with me, a MTB and my TT bike and was switching between them, but that was a more supported race – still the reason why I have SPD pedals on my road bikes so I can switch!)