What Happened On Friday

Friday after work I was waiting for the bus home when a woman with an unfocussed air approached me.
She kept looking up at the sky then sideways at me then up at the sky, bobbing her head up and down while just standing there silently. I saw she was dressed too lightly for the weather, with an open blouse and obviously no bra ... I was concerned she was going to flash me by accident or otherwise ... and carrying an open sleeping bag.
It didn't look right.
"Got a cigarette?" she mumbled at last. The words were slurred.
"No," I said truthfully, and "I don't have any money" untruthfully. It looked like she was going to beg for money which I don't give to people on the street. I want to help, but not to waste.
She stood there, mumbling and looking up then sideways then up.
I asked, "Do you need help?" I did not know what help to offer but it was obvious something was not right. Surely someone would be along I could refer her to.
She mumbled something I did not understand.
"The Union Gospel Mission can help. It's that way," I pointed. They had done some good work in the past with some people I knew. This wasn't much to offer but it's all I could think of.
She said, "Got a match?".
"No" I replied. "Where do you live?" Maybe she stayed somewhere that would take care of her and what a relief that would be.
"I'm homeless".
She put the sleeping bag around her shoulder and disappeared into the crowd.
I wasn't going to follow her and more actively insist she accept help from whatever source I could google on my smartphone, but I don't think that I handled this situation well. I don't know how better to handle it.
What would you do?