Yesterday afternoon I (male, late 30) went to the supermarket in my neighborhood to buy something. Since the sky was menacing rain, I took along an umbrella. Lucky me, when I got out from the supermarket it was raining, so I opened the umbrella and headed home.
Few meters ahead I saw a woman (looking about my same age) walking in my same direction without any umbrella. As I got close to her, I covered her with my umbrella and offered her to walk together. She thanked me and stayed under the umbrella, while making some small chat (how long are you being living here, the road works, the rain, etc.).
During the entire walk I tried to keep some distance from her (at least one palm between our elbows), despite the umbrella not being that large, just to avoid any creepy factor.
When we reached the second block (I live on the third) she told me she had to cross the road, because she lived on the west side on the road, while we were walking on the east side, and didn't want to bother me with crossing twice. So she thanked me again and had a short run under the rain to reach the opposite side walk.
I took it as a polite way of hinting me of not following her until her door, so I didn't insist on offering her some more shelter, and kept walking on my side of the road. However, later I reconsidered it as just being polite from her and not wanting to bother me and that I might have come out as rude for just walking away.
How could I have offered her if I could further shelter her from the rain without sounding creepy or pushy?