Since I'm male, I feel a little ludicrous leaping atop a soapbox and pontificating about budget travel for women.
Women do travel like that in every corner of the world.
No matter how obscure or inhospitable my destination, I always encounter women traveling alone or in pairs. In Albania, the only foreigners I met besides aid-workers and missionaries were two American woman hiking in the country's mountainous northern region. In Chiapas, Mexico, I met two young German women about to embark on a cross-jungle journey to Guatemala, which incuded a bus ride along hundreds of miles of unpaved roads and a trip in a wooden skiff down the remote Usumacinta River. I've also met many women who have traveled alone in India, South America, and Southeast Asia. The hardest part is buying your ticket.