Thank you very much Alex'in and the rest of the team, you really do a great job by so patiently answering all the questions... you're a great team!!! I'm happy to have chosen turkish as a 2nd language and studying it with your advice really makes it funnier and easy :) çok teşekkürler!
I am not Turkish, but I think your version would emphasize the number one, as if to say there was only one and not two... I might be wrong though. There was an example somebody had given before:
Büyûk bir sandviç yerim. - I eat a big sandwich
Bir büyûk sandviç yerim. - I eat one big sandwich.
Hope that helps.
in time i figured out that what women don't like about this word is its overuse. so while it is a synonym of hanımefendi it started replacing the word kadın nowadays. so sometimes while people use the word adam for men they use the word bayan for women which feels like they consider women to be 'well-behaved ladies' as opposed to real human beings by promoting sexism. this is what i understand from the current discussions on this issue. on the other hand it is completely okay to use the words bayan and hanımefendi when you want to say lady.
edit: and when addressing a woman directly (e.g. hey madam/lady) a woman might not like the word bayan and she might prefer hanımefendi. this is again about gender equality because when you address men directly (e.g. hey sir) you cannot say bay (and you can hear bayım nowhere but from the translations and dubbings), you can only say beyefendi. so it should work the same way for women. in short you should use the word bayan only when you can use the word bay for a man. also note that this is not as serious as the idea of the previous paragraph and women are almost always tolerant about this.
I totally get the frustration with the use of "lady" or any words that come "preloaded" with assumptions. In english, as i hear it here in the u.s., the phrase "what can i get you ladies this evening?" really weirds me out, it sounds oily and sexist, even tho intellectually i understand the waiter may have been trained to use these phrases...