What religion is it where the women wear a sort of bandana on their heads? I've seen them frequently in my area, are they a sort of Christian denomination?
Could be a house church, or any fairly fundamental 'born again' christian group.
They often cover their hair when attending a service, and also som of them do all the time.
Same reason as orthodox jewish women wore wigs when outside the family.
If it were in the U.S. and the "bandanas" were calico, the dresses were usually black or blue gingham, no make-up, they would most likely be Hutterites. A very industrious people that live together on communal farms. They originated in Germany, I believe, and, at least here, tend to speak German as a first language. They do their own schooling of their children as well...
I'd go with pega, Plymouth Brethren wear a small head scarf and always wear long skirts (never trousers or skirts above the knee). They also have to live in detached houses and not eat in front of anyone who is not from their Church.
women & girls who attend a local "I think" Lutheran Church, I think to do with German nationality, wear these headscarves bandana style. Sometimes gingham, sometimes pastel prints.