Have a look here: Meilleur, mieux, pire / plus mauvais, plus mal = better, best, worse and worst in French (irregular comparatives and superlatives)

‘Bien’ can function as an adverb, or as an adjective in limited circumstances.

It has a somewhat different sense when used as an adjective with state of being verbs  - (not always obvious to us non-native French learners). Some of its use seems more intuitive than teachable.

I may be wrong, but In your example, I would see the school being described in the abstract as ‘good’, rather than referring to the quality of the physical structure  - caring, providing good education and ‘environment’ for students, for example.

https://www.lawlessfrench.com/grammar/bon-vs-bien

https://www.wordreference.com/fren/bien