Does that mean I have to format the whole HDD to enable the bcache?
That's certainly what is suggested, yes. This is fairly common in RAID-like situations. You start by generating a new mapped bcache device and then you format that, instead of the hardware directly.
However, the other RAID-like things (mdadm, dmraid, etc.) have documentation that make it quite clear how you create one of these setups and then install on top of it (and have
initramfs load the right stuff so you can boot!)
I'm fairly experienced messing around with bizarre file system arrangements and kernel modules, but even I wouldn't want to touch this, especially not if I was trying to retrofit it into an existing installation.
I would concentrate on what I've got in front of me. If your SSD is fast and of a moderate size ~10GB+, stick Ubuntu on there and host
/home on the spinning rust. That should give you some room for installing things, though you might have to move
/opt to rust at some point. It may seem complicated now, but it's quite easy to split an installation over multiple disks.
If the SSD is tiny (<8GB) and/or slow, it may be worth considering just not using it.