Final answer:
The correct way to offer assistance is to politely approach and offer help with crossing the street, allowing the old lady to accept or decline the offer.
Step-by-step explanation:
To express assistance to an old lady carrying a large bag and trying to cross the street, the most appropriate and respectful approach would be a) Politely approach and offer help with crossing the street. This shows kindness and consideration for her potential needs without making presumptive judgments about her capabilities. It also allows for a personal interaction where she can either accept or decline the assistance based on her preference. In contrast, options such as ignoring the situation, shouting from a distance, or taking a photo do not provide immediate assistance and may be intrusive or inconsiderate.