Make a backup of your system before upgrading. Or don't… I don't care.
1. Modify APT's source file to point at the Bullseye repos.
/etc/apt/sources.list
The old, Buster, config:
deb http://deb.debian.org/debian/ buster main
deb-src http://deb.debian.org/debian/ buster main
deb http://security.debian.org/debian-security buster/updates main
deb-src http://security.debian.org/debian-security buster/updates main
deb http://deb.debian.org/debian/ buster-updates main
deb-src http://deb.debian.org/debian/ buster-updates mainThe new, Bullseye config:
deb http://deb.debian.org/debian/ bullseye main
deb-src http://deb.debian.org/debian/ bullseye main
deb http://security.debian.org/debian-security bullseye-security main
deb-src http://security.debian.org/debian-security bullseye-security main
deb http://deb.debian.org/debian/ bullseye-updates main
deb-src http://deb.debian.org/debian/ bullseye-updates main2. Upgrade packages to prepare for the system upgrade.
apt update
apt upgrade3. Upgrade from Buster to Bullseye
apt full-upgrade4. Reboot the system.
shutdown -r nowDone.