There has been much noise about gender segregation on busses in Israel. Most authorities seem to agree that it is permissible to sit next to the other gender on public transport, so there is no obligation to have segregated busses. Individuals may of course decide for themselves if it is a problem for them.
Two halachic opinions:
Consequently there is no need to refrain from traveling on subways and buses to go to work when they are very crowded and it is not possible to avoid contact with women. That is because contact without intent for pleasure that results from the inevitable crowding and pushing is not done in a licentious manner (derech chiba)…. Similarly there is no prohibition for this reason to sit next to a woman when there is no other place available. That is because this is also not done for the sake of pleasure (Igros Moshe, Even HaEzer 2:14)
Seemingly, from an aspect of modesty, segregating buses and streets is advantageous; however, its damage exceeds its benfits, for a number of reasons:
First, all issues of ‘hiddur mitzvah’ should be personal acts, […]
Secondly, when some people are negatively affected by the ‘hiddur’, the damage caused is immeasurably greater than any benefits. […]
Thirdly, this type of policy harms proper family behavior. […]
Fourthly, when dealing with the laws of modesty, special care must be taken, for sometimes additional laws are liable to arouse more forbidden thoughts. […]
(Rabbi Melamed: Gender Segregation on Buses is Not Jewish Law)
More opinions can be found in Yeranen Yaakov: Men and Women on Buses – Contemporary Rabbis’ Opinions.
As last words, I want to add that there is never a reason to be rude or to embarras someone. It’s very easy. If you get on a bus and look for a seat, just chose a seat next to someone your own gender. If there is none, stand. If there is an empty seat next to yours and someone of the other gender sits down, keep focused on your book or get up (if you think this is rude, offer your seat to someone old, say you’ll anyway get off soon, …).