I got a bit of a history of religion background. While I cannot give you any sources on the top of my head (it has been over a decade since I took history of religion at college), the connecting factor is that Islam, Christianity and Judaism are considered Abrahamitic religions. There are some common elements to all three faiths, such as the belief in one god only and in the belief of the prophets of the old testaments. In the case of the hijab and the babushka, both the bible and the quran tell women to cover up.

In the bible women are told to cover their head in both the old and the new testament. Both religious jews and religious christians follow this.

Jewish women cover their hair all the time after marriage, they wear a hat, a scarf or a wig. In the synagoge and during prayer male jews wear a kippa and a prayer scarf, also covering their head.

Spanish catholic women used to wear a mantilla for the same reasons and there are some deeply christian people in the US who also cover their hair. (Think hutters, mennonites. See the onlineshop http://www.christiancoverings.com/ for examples.) Most prominent example of christians covering up are probably catholic nuns - "taking the veil" is a sign of commitment.

So the tradition for the slavic babushka is deeply christian, but the majority of christians no longer cover their hair. Only muslim women do.

So while there is a connection between the hijab and the babushka, it is not specific to the head covering. It is based upon the same general connections Islam has with Judaism and Christianity.

If you are interested in this, read up some more on the origins of islam. I can point you to some books if you want me to.