I can install ibus-libzhuyin using sudo eopkg install ibus-libzhuyin, but, even after enabling it as an Input Source in the Region & Language window via Chinese (Taiwan) > New Zhuyin and then rebooting, it doesn't appear to work in Solus 4 Budgie; there's no option to select it in the Keyboard Layout applet.
(On the other hand, I can get the Spanish (United States) > Latin American Input Source to work without issue. Also, ibus-libzhuyin works in Ubuntu 19.10, so I'm guessing that this is a bug in the Budgie desktop.)