If you are bothered about something, it is important to you and you are worried about it.

He's very bothered about what people think of him. 他很在意别人对他的看法。

They were an hour late and she didn't seem at all bothered. 他们迟到了一小时，可她似乎一点也不在乎。

The bright sunshine made him feel hot and bothered (= hot and uncomfortable). 灿烂的阳光使他感到很热，很不舒服。

If you are not bothered about something, it is not important to you or does not worry you.

"Tea or coffee?" "Either - I'm not bothered." “你要茶还是咖啡?”“随便──都可以。”

I'm not bothered whether I go or not. 我去不去都无所谓。

You choose something for dinner. I'm really not bothered.

Honestly, if you'd rather we didn't go to the party, I'm not bothered.

I told William to make a decision about which apartment to rent because I'm not bothered either way.

If you'd rather stay at home, I'm really not bothered.