I witnessed an Islamophobic attack for the first time - did I do the right thing?

As-salamu alaykum. I'll try to explain what happened as clearly as I can. Sorry if it's a bit long. I live in a Western European country. Yesterday I was on a bus. It was almost empty - just me and a sister wearing a hijab. She was sitting at the back and I was at the front. At one stop an older woman got on. I started hearing voices from the back. At first I didn't pay much attention, but the tone got louder so I turned around. The old woman told the sister, “Aren't you ashamed with that rag on your head? Go back to your country.” I decided to go over and ask what was happening (yes, maybe not the best phrasing, but I wanted to help). The old woman said to me, “No, but sir, surely I'm not right? I'm fed up with seeing this,” pointing at the sister. I'm of mixed African/European heritage (100% Muslim) and I think the old woman assumed I wasn’t Muslim. I told her her behaviour was unacceptable, that you can't attack a young woman for no reason, and reminded her she was also in this country. I also noticed the sister looked European. The old woman answered with spite, “Everyone's always there to support them, but she has no business being here with her religion, wearing the veil is a disgrace,” and things were getting heated. The bus driver ignored it. At the next stop an Arab sister boarded and immediately asked what was happening; she gave the older woman a small push, maybe thinking I was challenging her. The younger sister and I explained and the new sister became more vocal with insults. The older woman went pale and her hands started to shake. I could see the situation might explode. I told the older woman to apologise to the young sister - I hoped that would calm things. Then I told her to get off at the next stop; she did. The second sister seemed ready to get off and follow her, but I persuaded her not to. It all happened in less than five minutes. Looking back, I feel like I stood up for the young sister and also prevented a bigger confrontation. I think I did the right thing by defending her and trying to defuse the situation, but I'm not sure if I handled it perfectly. What do you think - did I react correctly?