If you're going to be like that, you might as well say English doesn't even have the passive voice! But clearly it does; the verb "to be" is used as an auxiliary when constructing it, but the passive voice certainly exists.

And "be bothered" is clearly passive in construction, but its meaning is closer to "bother" than literally "be bothered [by someone else]". I think it qualifies pretty well as a deponent verb, therefore.

Don't mind me, I don't do English grammar :)