A little history
Back in the 70's, when we typed a letter we would put three pages in the typewriter (yep, we would manually feed them into a typewriter, no computers or printers back then)! The first page was letterhead, the second page yellow and the third page blue. A carbon paper would be inserted in between each and when typed on, it would print onto all the pages. Hence the reason it was called a "carbon copy". Today we still use the cc, but it is commonly referred to as a "courtesy copy", although I have still heard it referred to as a carbon copy.
My memory is failing me a bit here, but I believe the yellow copy was the file copy and the blue was the cc or bcc to be sent out. They were commonly called the "yellows" and the "blues".
Whether you refer to a cc as a courtesy copy or a carbon copy, the most common way I have seen it typed is c.c. or b.c.c., but I have also seen it c:, bc:, cc:., bcc:, c. or b.c.
b.c.c. refers to a blind carbon copy. This would not be typed on the letterhead copy, but would only be typed on the file copy (to have a record on the file that you sent it out to other people) and the copy you are sending to the other person (or people). You would use a blind copy rather than a cc if you did not want the person you were writing to, to know you were copying someone else on the letter.
I was reading an article1 by Kevin Laurence that you might be interested in reading.
1 Laurence, Kevin, The Exciting History of Carbon Paper, http://www.kevinlaurence.net/essays/cc.php, (accessed November 2, 2007)