Which is correct?
The "idea" of walking out is singular so i chose the latter
which one of them is it right?
That she walked out when he arrived bothers(bothered) me. Bothers is prefferable in that it is a present state of mind. On the other hand, bothered is also possible on account of the agreeing verbs in the past preceding the "bother"
The subject is third person singular so the verb is used accordingly.