You have already reached the Ashram, why are you still thinking about that old lady now? Just relax. Yes, you should always honour and respect women, and be considerate towards children and the elderly. Always respect your elders and senior citizens and give them consideration. This has been the custom in our country since the ages.
In the past 8-10 years this custom has started to disappear from our culture. Nowadays you will see that a young boy will keep sitting in the bus while an elderly person will stand throughout the journey. During my school days, whenever any elderly or senior person used to come, we would immediately stand up and offer them our seat with respect. This is unique to Indian culture. It is not so in the foreign culture. In foreign countries, young people remain seated in buses and trains while the elderly have to stand.