my daughter learned on her own at 3 months almost 4 too. I think it's because they're at that stage where they're curious to touch and hold things. she's 5 months today and still holds it and now knows how to also push the bottle away from her mouth. :)
I was going to ask how you got her to hold it too. My daughter is 8months old and won't hold her own bottle. She'll pick it up and play with it and bring it to her mouth but then let's go. LOL. She is also good at pushing it away when you are truing to feed her as well.
I think it's just the fact that she keeps trying to put her hands in her mouth. Sometimes she holds it, sometimes she doesn't but I'm impressed that she did such a good job so young. I didn't think she would be able to until she was 6 months or so. She will be 4 months on the 11th