biting her baby sister

My dd, who will be 3 in July has started biting her little sister.

We have never had any issues with her except for this and smacking her sister.a few weeks ago

I think the first time this happened it was quite by accident. Not knowing exactly what had happened to the baby at the moment I made quite a fuss and then she told me she had bit her fingers. I was shocked.

Since then she has bitten her twice more, once on the fingers, once on the cheek...baby is 5 mos old btw.

Right now I am keeping baby really close to me all the time but something tells me this is aggravating the situation as I can't let dd get close to me when I am wearing baby(one bite happened while I was holding baby...I thought she was kissing her and she bit her

After the last bite my dd was walking around saying "I shouldn't hurt my poor little sister" and acting really contrite and remorseful but I know she will do it again.

She also tries to put her feet in her face which I think will lead to a kick eventually.

I am trying to keep up on snacks and watching that she gets plenty of sleep.

I am not sure how to stop this. I can't ignore this behaviour completely...I have to remove her from her sister.

All three times this happened it wound up with crying baby and tantruming toddler.

I am hoping this just goes away.

But anything I should be doing in the meantime?