|Rather than a suggestion, here is a question back to you: do you need to have communication with her? In the first place, it does not sound like you committed a heinous corporate crime by asking her to handle a task that suited her skills better than yours. Unless your email had a nasty tone, she is grossly overreacting to this matter.|
Secondly, you apologized to her, did the actual work, and came back bearing a gift. This leads to the second question: how much more must you do? At this point, you can be cordial and polite to her, but stop the groveling. You should deal directly with her manager on your projects.
And speaking of her manager, you should discuss this matter with him. He needs to let her know that her behavior is counterproductive and must stop now. If he does not or cannot get this message across to her, that raises even more questions about him and her. Either way, with the passage of time, this storm is likely to pass, too.