Legal Question in Constitutional Law in New York

Private businesses can set dress codes and refuse to serve customers who violate them. There are limits to this freedom, though. In particular, a public accommodation (like a bus company) can't discriminate on the basis of race, religion, etc., even if it disguises that discrimination as something else.

But that does not seem to be what happened here. It does not sound as if the bus company cares whether its passengers are Jewish as long as they are dressed modestly and sit with their own gender. The type of clothing that would satisfy them is not religious in nature. If I'm right about that, then the company's actions were probably legal.

The separation of men from women might be an issue if one gender gets better seats than the other. But that does not seem to be what you're asking about, and you haven't provided enough information to address this topic.