Usually you have an image of the Raspbian version that you can download from https://www.raspberrypi.org/downloads/raspbian/ or from https://downloads.raspberrypi.org/. But as far as I know there is no image available for the testing version Raspbian Bullseye so you have to install it from the repository.
There are two ways to install Bullseye from the repository:
full upgrade from Buster
bootstrapped from the repository
I prefer to use bootstrap because then you have a clean configuration and not modified old (from Buster) configuration files. How to do it you can refer to Install base Raspbian from repository, not using an image but I haven't tested it for this answer. So I will look only at the full upgrade.
There may be an additional problem with the firmware. I also haven't found specific one for Bullseye at http://archive.raspberrypi.org/debian/dists/ but that is needed of course. So I try to use that for Buster.
Upgrading from Buster is very easy. Just flash a fresh Buster image, boot it in your RasPi and update it:
rpi ~$ sudo apt update
rpi ~$ sudo apt full-upgrade
rpi ~$ sudo systemctl reboot
Then just modify the first line in /etc/apt/sources.list
# from
deb http://raspbian.raspberrypi.org/raspbian/ buster main contrib non-free rpi
# to
deb http://raspbian.raspberrypi.org/raspbian/ bullseye main contrib non-free rpi
Don't touch /etc/apt/sources.list.d/raspi.list
so you will use the same kernel and firmware compiled for Buster.
Then execute again:
rpi ~$ sudo apt update
rpi ~$ sudo apt full-upgrade
rpi ~$ sudo systemctl reboot
Login and check:
rpi ~$ lsb_release -a
No LSB modules are available.
Distributor ID: Raspbian
Description: Raspbian GNU/Linux bullseye/sid
Release: testing
Codename: bullseye