If you see the child in question acting inappropriately I don't see why you cannot step in (especially if the childs mother won't) and in a low tone voice just say "biting is not nice" or " do not bite" just something .... if the mother gets upset you then have a window to discuss the childs previous outbursts.

I have scolded my niece for her rough behaviour but I do let her get rough with DD to a point as well just to see if someone steps in. If they don't I have no issue with it and I usually say something just loud enough for SIL or MIL to hear.

A few times niece has dug her nails into my face and I have really growled at her and had her in tears, there is little parents can say when they can plainly see the marks!

Nae x
This is what I'd do. Afterall the protection of your DD comes first, and it's not like your belting the living daylights out of this other child. By the age of 4 she should really know that biting other kids isn't on.