Collocations for bored - adj.

be, feel, look, seem, sound
become, get, grow
Some children get bored very quickly.

remain

extremely, fairly, very, etc.
terribly, thoroughly
a little, slightly, etc.

at
bored at the prospect of going shopping

by
He seemed slightly bored by the whole process.

with
He was bored with their conversation.

bored rigid (BrE), bored silly (BrE), bored stiff, bored to death, bored to tears
I remember being bored stiff during my entire time at school.
She was alone all day and bored to death.

bored out of your brains (AmE), bored out of your mind, bored out of your tiny mind (BrE)
He walked along, bored out of his mind.

Bored is used with these nouns:
expression, teenager