have (esp. BrE)
I had a little bother finding your house.

cause, give sb (both esp. BrE)
Your little boy didn't give me any bother.

go to
I wouldn't go to the bother of making the cakes myself.

put sb to (BrE)
I'd love to come and stay with you, but I don't want to put you to any bother.

save sb
Getting a taxi will save you the bother of picking me up from the station.

without any bother (esp. BrE)
We found the hotel without any bother.

bother to
I don't mind taking care of your dog—it's no bother to me.

bother with
He's having a little bother with his computer.

a bit of bother, a little bother, a lot of bother, a spot of bother (all esp. BrE)
He's in a bit of bother with the police.

no bother
It was no bother having the children to stay.

Bother is used with these nouns as the subject:
conscience, injury

Bother is used with these nouns as the object:
head