Since the word ĝeni means "to bother, to annoy", what would annoying be? (Ex: She is so annoying)
Would it be ĝenanta or ĝena?
Ĝena can be used as an equivalent to ĝenanta. However, ĝeni means "to hinder" and by extension, "to bother, distract." In the Plena Ilustrita Vortaro, the definitions are:
1 Malfaciligi aŭ malhelpi ies movojn To make someone's movements more difficult
2 Malfaciligi ies agojn, pensojn ktp per ne materiala malhelpo To make someone's acts or thoughts more difficult by non-material means
Therefore, strictly speaking, ĝenanta means "bothersome" in the sense of hindering, or distracting.
If they are not getting in the way, or distracting, then you could try iritanta ("irritating"). So I would suggest Ŝi iritas min (tiom).
Related words are ĉagrenanta ("upsetting, vexing"), incitanta ("teasing"), tedanta ("boring, over-persistent, repetitious").
The commenter 2_K_ suggests agaca, which I forgot about completely.
The adjective form of ĝeni is ĝena.
The word ĝenanta is, of course, possible, but you'll rarely find it used as an adjective, which is what you're asking.
More often, ĝenanta is used to show action:
li ne estos ĉiam ĝenanta kaj muĝanta (he won't be always getting in the way and grumbling.)
[ŝia koro] volus disŝiri la tunikon, ĝenantan la bruston.
A person who is habitually annoying could be called ĝenema.