I don't think a man needs to give up his seat on a bus for me, just because I'm a woman. I'm usually perfectly capable of standing. And when I'm not, I see to it that I don't stand. I will either wait for the next bus, or go grab a taxi. It is not up to perfect strangers to see to my needs.
And I've seen many a kind stand on the bus, when there was plenty of open seating. Lots of them think it is fun. If it is dangerous for them to stand, then I really hope their parents wouldn't drag them onto a standing room only bus.
Well, that is your choice but it is proper etiquette and even my almost ten year old DS would stand to give a seat to a woman with a small child or an elderly woman. I'm proud that I have taught my sons that respect and I'm often saddened by how many "modern" families think those polite little tidbits are old fashioned or out of style. FYI, both of my sons would hold a door open for a woman too.
When I said "small child", I meant "babe in arms", not a five year old because yes, some of them truly enjoy standing.