The Beginnings of a Bully

I need some advice.

Yesterday my 1st grader (Gwen, you probably know her...) came to me with a bit of a problem. In her class there's this girl (we'll call her Barbie) who doesn't have any friends. She told Gwen that she was her only friend and wants to spend all her time with her. I love that Gwen is an accepting and obsessively social girl who wants to be best friends with everyone, and I encourage that. But there's a reason little miss Barbie is friendless. She's a little bully. She got mad at one of Gwen's other friends (Peanut) and told Gwen she can't be friends with her anymore. Gwen told me she's scared of Barbie and told her she wouldn't be friends with Peanut, that she didn't like her anymore. Barbie had actually punched Peanut in the stomach earlier in the year that went untold, and Gwen doesn't want to be punched. But Gwen said she secretly was still friends with Peanut and would make sure Peanut knew it. But it would all be hush hush.

Of course, I told Gwen it's more important to stand up for herself and for her friends and not be scared of being hit. If she hit her, she'd tell a teacher and me and that little bratty Barbie would be home schooled from that point onward. (Or I said something along those lines.) Gwen seemed a bit nervous but agreed, and we made a plan that if she told Gwen she couldn't be friends with Peanut again to say, "I still want to be friends with Peanut. But don't worry, Barbie. I'll still be your friend, too." I mean, this girl is only 6 or 7, and she's telling my daughter that she secretly wants to be a Bad Girl and wants Gwen to be a bad girl with her. (Fun fact: when I was a kid, I was in a Mischief Maker club with a friend and we'd go around and do little things here and there for tee-hees and giggles. It's not a big deal, I guess little kids like the thrill of it.) But Barbie is already taking shots at people and I'm not liking her sort of mischief.

BUT.

I told her to still be friends with her. Is that wrong? Gwen's her only friend and she's pressuring Gwen to do wrong things, but they are only 1st graders. Gwen is a very strong personality and won't do anything she doesn't want to do, and if this Barbie girl has a real friend who genuinely wants to be her friend and love her until the end of days with her hundred other best buds, I think it'll be the best thing for Barbie. Or am I crazy? Should I tell Gwen to stay away from her, to be nice, but find somebody else to play with? I find that a bit harsh, especially since they are so young. Maybe Barbie won't turn into such a bully if she had a nice friend. Or is there a good chance Gwen will start acting up with her if she keeps playing with her? What would you do?