Who, or more precisely, what is a Lady?

Would you refer to yourself (or, if you happen to be male, would you refer to a female) as a lady or a woman or would you rather use the term 'girl'?

I mentioned to a friend the other day that I belong to a Ladies' Bridge group. She frowned. I assured her that it was a perfectly civilised group, no glaring if one of us makes a wrong bid, no shushing if any of us get the giggles. It was social bridge with an emphasis on the word 'social'. She explained that her frown was for the name rather than the activity. It should, more accurately, be Women's Bridge.

I took this on as a challenge. What is the difference between the two and what about the word 'girl'? Should we maybe call it the Girls' Bridge group instead? 

Lady, according to the Oxford English Dictionary, can be used in many ways:

• It means the wife of a Lord. That's not us! 
• It can be used in a derogatory way, e.g. "Listen, lady, I've had enough of this!" Ladies who lunch started out, I believe, as a mildly insulting term implying that the ladies have nothing better to do. (I think it's an excellent activity, myself.)
• It is used in a formal setting when welcoming ladies and gentlemen to a gathering. 
• It can be used when referring to a young girl with attitude, e.g. "You're asking for trouble, young lady!" 
• It is even used as a modifying term, e.g. lady doctor

But the word does not, apparently, describe a group like ours.

The OED is no more encouraging about the word 'woman':

• It is used as a general term, e.g. women's department in a clothes shop. 
• It can be used in a patronising way, e.g. "Pull yourself together, woman!" 
• What really puts me off the word is the 'old woman' tag. I don't care how old I am in actual years, I will not be classed as an old woman (grumpy or otherwise) for at least another 20 years, so there! 

It would seem that our group cannot be referred to as a Women's Bridge group either.

I glanced at the definition of 'girl' with little hope for a resolution to the problem. This is what the OED said:

• a female child, a daughter or a young woman. Sadly, we're not the latter!

And then I saw it...

• a social female group, e.g. having lunch with the girls.

That looks like a clincher. We should, from now on, be referred to as the Girls' Bridge group but somehow I don't think it's going to catch on!