Bother indeed has both transitive and intransitive senses, and they all have the general sense "trouble"; but they are used in slightly different ways.
Transitive bother means to "cause trouble" for a person, who is cast as the direct object. When the subject is an animate agent, it typically means to annoy the DO by intruding on the DO's activity; when the subject is inanimate, it typically means to worry the DO.
My little brother won't stop bothering me when I'm trying to work.
This proposal bothers me.
Intransitive bother means to "take the trouble" to do something. It is typically used only in negative contexts.
Don't bother to clear the table; I'll put my stuff away in a minute.
If she won't bother to tell us what the problem is I don't see how we can help.
None of your three sentences is quite idiomatic. The first has no negative to trigger use of bother; the second lacks a passive auxiliary (was or is bothered), and the third lacks a negative and the obligatory infinitival complement.
Ergative is occasionally used to categorize verbs like bother, and I used it back in ELL's early days; but it has a distinct technical meaning in other contexts, and snailplane suggested a better term: labile.