Where can I direct a single homeless woman to a safe shelter?

There is a woman who has been staying on the side of the road near where I work for the past few days with all of her personal belongings tied up in reusable shopping bags. Yesterday I gave her a bottle of water and a couple of dollars and spoke to her for a few minutes, she told me that she was recently ejected from her housing situation because of "vandals", (not really sure what she meant by that) and is looking for a safe place to stay. She seems to have issues with her memory. She kept holding her head and thinking really hard when I would ask her questions, saying that she was trying to remember. She kept saying she wanted to stay near Sage Road. She mentioned it in conversation four or five times. Her manner of speaking made me think that she might be suffering from some sort of mental health affliction. I hate the idea of her staying on the side of the road alone with all of her stuff, I've been trying to contact SEARCH and Star of Hope this morning but I can't get a hold of anyone. Would it be advisable to bring her or arrange for her to be shuttled to one of these places? Do they have resources for vulnerable folks like her? A place to stay? She doesn't have a phone so she can't contact these places herself and I'm a bit concerned that someone is going to call the police on her at some point because the neighborhood she is hanging around in is very close to the Galleria. Any advice would be appreciated.