You need to think of what is most important to your child, what is more important to her. When she's a bully, do you put her on your lap and talk about it or do you just put her in a time out? Two important things must happen:
1) She must know that no matter what you love her - so don't raise your voice to her
2) You need to enforce your authority. She needs to know that you mean what you say and why you say it. She needs to know that what is wrong is no ok with mom and dad.
She has learned that there are many things that you allow simply because you love her. If you don't correct this now, she'll get worse as a teenager.
When there's a time out:
1) Put a small chair in the corner, facing the corner
2) Walk her to the corner and sit her on the chair. If she gets up, tell her NO firmly and reseat her in the chair. Tell her that she is to stay in the chair for 5 minutes and you will come for her. NOW - walk away, don't look back until you're away from her line of sight. If she gets up again repeat the process. She's no learning the lesson until her actions change. When she really understands, she'll cry because she doesn't like being in the corner and alone. Don't feel sorry for her, because her actions are that of a big girl and won't be allowed.
3) when time out is done, sit down with her and explain to her, not at her, what she did wrong and that you love her.
You really need to be firm with her or she won't learn.
Old mom.