How can i fix this friendship?

First of all, you should make sure that your girlfriend know you and the girl(i will call her miss A) are "pure friend". After you clarify the relationship, i'm quite sure that your girlfriend will be ashamed and regretful about what she has done, as it hurts. if she find it's embarrassing to apologize, you can encourage her to use sms/ whatsapp, so face-to-face communication can be avoided. but most importantly is that, you need to let her know you care about miss A's feeling isn't because you have a special feeling on her, just because you and miss A are friends.
Miss A may have hard feeling now, you may have to spend more time to tell her you feel sorry about that, and promise it won't happened again. just ask her out for a dinner(she may ignore you if you text). give her some time, maybe she need to re-think about how to handle this friendship.
By the way, if I were you, I’d spend some time to talk with the girlfriend. You know if she is oversensitive, this is harmful to the relationship. You have to emphasis that you need personal time, and it’s impossible for you to avoid contacting all female friends, you love her, but at the same time you need her respect.
hope it helps. You are always welcomed to inbox me if you need more advice:)

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Less is more.

Your friendship will not need to be fixed if you've apologized already.
Haven't really been spoken to your friend after the incident is the best thing to
do, because:
1) It can avoid further misunderstanding
2) You can save your friend from embarrassment among all common-known
friends

Just remember to send her birthday greetings and resume contact when your
girlfriend has trust on you.

Somehow, one can't be too greedy. You can't please everyone at the same time

I believe there must be a reason for your girlfriend to act like this.
Reckon if you should solve your problem ahead (your girlfriend) before digging
another one (your friend).

By the way, you don't have to worry too much if that's your real friend. She will
understand ... unless you've had ambiguous relationship with your friend and
you are too used to the 'flirtatious' chat with her almost everyday…

XD

Good Luck.