'Worry' means to be anxious or concerned. 'Bother', in this context - where the speaker is the SUBJECT of the sentence - means to 'take the trouble' to do something, in the sense of expending time and energy. For example, if you say 'He doesn't bother to reply to my emails' this suggests that he is too lazy or rude to reply. He doesn't think it is necessary to take the time and trouble to reply. In your sentence, the only way that 'bother' makes sense is as a rhetorical question: 'You're going to do whatever you want. So why do I bother?' The speaker is asking himself or herself why they should take the trouble to give advice to the other person when the other person is going to ignore it. As Leuriza suggested, it's the same as saying 'Why do I even try?'. This meaning of 'bother' is a very different meaning from 'worry'. When the person is the OBJECT of the sentence, however, then 'bother' can have the same meaning as 'worry'. For example, 'It worries me' and 'It bothers me' do have a similar meaning. However, this is not the sense in which 'bother' is used in this particular sentence.

In this sentence, you could also say "why do I even try?"

It bothers me that he is acting like a jerk. It worries me that she is up on that dangerously high ledge and could get hurt. Does that help?

your sentence

you sentence is very good