In Israel, most public transport shuts down on Shabbat.
If it did operate on Sabbath, perhaps by non Jews, would it be permissable for Jews to use it on weekdays?
I do not see why it would be not permissible to use it. No one has a problem using electricity during the week, which the electric company is operating on Shabbos too. No one has a problem using the telephone during the week, which the phone company is operating on Shabbos.
The only possible reason that some people might have not to use it during the week, is that they feel that by not using it during the week, it would make the company not run on Shabbos.