GNOME desktop has IBus integration by default. To set up the Zhuyin/Bopomofo (注音) input method is quite easy. On Arch-based Linux, there is an AUR package called
ibus-chewing which is a Chinese Zhuyin/Bopomofo engine for IBus. The engine uses
libchewing(酷音) under the hood. It's also a very popular input library in Taiwan, even on Windows systems.
ibus-chewing package from the community repository:
sudo pacman -S ibus-chewing
yay -S ibus-chewing
Don't know how to install packages on Arch-based Linux? A full guide on Two Ways to Install Packages from AUR on Arch Linux/Manjaro.
In Keyboard of GNOME Settings, add Chinese (Chewing) in Input Sources:
You might need to reboot after the installation if Chewing is not present in Input Sources.
Super+Space to switch your input methods, or select it in the taskbar:
Extra configuration could be found in Preferences of Chewing: