Describes a person's disposition: easily embarrassed, self-conscious, or prone to blushing. Often used with ～な人 or ～な性格.
He is bashful and not good at speaking in front of people.
照れ性な性格を直したい。
I want to overcome my shy nature.
He's a bashful person, and his face turns red as soon as he's praised.
My little sister has a bashful personality and isn't good at speaking in front of people.
I'm too bashful to easily tell someone how I feel.
内気 describes a reserved, introverted personality in general, whereas 照れ性 focuses specifically on becoming embarrassed or flustered in social moments.
シャイ is a casual loanword meaning shy, often used lightly or affectionately, while 照れ性 is a native term describing an ingrained bashful disposition.
大胆 describes someone bold and unafraid of attention, the opposite of the easily-embarrassed disposition described by 照れ性.
照れ屋 is a noun meaning 'a bashful person', while 照れ性 is used adjectivally (照れ性な人) to describe the trait itself.
Compound of 照れ (bashfulness, from verb 照れる 'to be shy/embarrassed') and 性 (nature, disposition).