What about simply doing what Monsey Trails does and having men on one side of the aisle and women on the other side of the aisle. Very easy, there’s no concept of ‘moving back’ in a negative way, etc.
Personally, as a ‘spoiled suburban kid’ I barely ever take the bus, but it seems to me that the way things that are gender separated and stuff like that are done is by mutual consent. I know before I buy a ticket on the Monsey Trails that when I get on, I’m going to need to sit on the right-hand side on the bus. If I didn’t want to do that, then I would find some other way to get where I want to go. The difference here, on a public bus, is that unless there is MORE THAN ONE bus, going the same route as the gender-separated one, to give people the option of sitting as a family or something, or it is obvious and known that this is a gender-separated bus (as this one seems to be), it really can’t be sustainable. A non-frum Jewish woman may want to sit with her husband/boyfriend/older son in whatever section of the bus, and I don’t know how the system works in Israel, but it seems as though she has that right, especially if Egged is a city bus service that they’re paying for with their tax dollars/shekels.
It’s a similar reason (according to this theory which I’m not going to swear to due to possible lack of understanding) that there’s no religion in schools. Everyone, of all different ethnic backgrounds, pays taxes that go to the school. If that’s so, then it’s not fair to force the child of a taxpayer to conform to the religion of a different taxpayer who’s paying the same taxes.
So Health, sure, go ahead and ask the non-frum lady next to you if she’d mind moving. But it’s quite within her right to refuse without it being called charedi discrimination.