I thought it was cúthalach
It’s not in Dinneen’s dictionary, but there’s a song called An Baitsiléir Cúthalach, so perhaps it’s a dialectal variant of cúthail.
EDIT: See the comments here.
Focloir.ie doesn't give that, but I seem to recall reading it in some of Ó Conaire's works...
Why does chúthail have a h?,
Attributive adjectives agree with the noun that they qualify. Because bean is a feminine noun, it's adjective has to be feminine too, so the adjective takes a séimhiú to indicate the gender.
What about if the sentence is "The woman is shy", would 'cúthail' also agree with 'bean'?
That's a predicative adjective. (In English, attributive adjectives come before the noun, predicative adjectives come after the noun).
Predicative adjectives are not modified - they don't have to agree with their nouns.
I didn't know about predicative adjectives not having to agree with their nouns, thanks