Traditionally, Turks would use

xxxx bey and xxx hanım for a Turk

and

bay xxxx and bayan xxxxx for a foreigner.

So someone being formal would call me Bayan Marion.

But the distinction is now more blurred and Marion Hanım is also used today.

Not exactly correct.

Marion is right in saying the distiction is somewhat blurred today.

Every man normally qualifies for the title of "Bay", like every woman can normally be referred to as "bayan"; they both are solely gender referenced titles.

Traditionally however, titles "Bey" and "Hanim" also refer to the (higher) social status of that person, apart from his/her gender.

Good explanation...I would like to add a tiny thing to it: We also use bay/bayan for Turkish citizens of Christian or Jewish faith: Bay Yasef, Bayan Rachel, Bay Garo, Bayan Ağavni, vs. 

I would not advice you calling your Jewish boss "Bay Yasef"...He may not appreciate it, if his Turkish is any better than yours...

If Bay Yasef was my boss (unfortunately not), I would address him as Yasef Bey. But he is my friend since we were a high school student and I often address him as ulan i**e   Bay Aram (an Armenian) is my next door neighbor and I address him as Aram Abi. And we call him Aram Bey in his absence.

By the way, I wouldn´t mind if their Turkish were any better than mine since they are native speaker of Turkish.  

Do you still have difficulty in getting my point? Don´t you live in Turkey? Don´t you read newspapers? It is not me but they themselves who prefer to use bay/bayan. Look at this:

http://www.google.com.tr/search?q=%22vefat+bay+ve+bayan%22&hl=tr&ei=a9XrTOOBGYiM4gbT3bCDAQ&start=0&sa=N

Anything else?