It would be helpful to find out what is causing her to lash out at other. Is she feeling intimidated and is protecting herself, is she frustrated and unable to otherwise feel heard, is she anxious, etc.
You are already using a behavioral modification at home and educating her on bullying. Try to assist her in identifying her feelings and then finding healthier options to express herself. You can engage her during play or artwork to solicit some information as to what is going on in her mind. If you decide to do a pretend play, you can let her act the the role of the teacher and you the pupil. Then, switch around the roles where both of you are the children in a pretend class (it may be easier to use her dolls for this activity) and monitor to see at what point or what triggers the changes in her behavior to become frustrated.
You can teach her about healthier ways to express herself or anger management techniques such as breathing, walking away, counting to 10 in her mind, thinking before acting and especially thinking about the consequence for aggressive behavior.
A Volcano in My Tummy: Helping Children to Handle Anger - Paperback