doesn't bother me any

(It) doesn't bother me any.

 and (It) doesn't bother me at all.
It does not trouble me at all.; I have no objection. (Compare this with (It) don't bother me none. Not very polite or cordial. See also (It) won't bother me any. for the future tense of this expression.) John: Do you mind if I sit here? Jane: Doesn't bother me any. Sally (smoking a cigarette): Do you mind if I smoke? Bill: It doesn't bother me any.
See also: any, bother