"Bosom" is generally used to refer to the chest area of a person, and therefore the singular is usually used. However, there has been uses of the word "bosoms" to refer to the "breasts" of a woman:
2003, Martin Kelner, The Guardian, 7 Apr 2003:
The prevailing look at Aintree was of a well-upholstered woman wearing an outfit about three sizes too small for her; trouser suits so tight you could not only tell if the lady had a coin in her pocket but see if it was heads or tails, and skimpy tops proclaiming proudly that bosoms are back - and this time it's personal.
This seems however, to be a relatively new usage. Wiktionary defines it as:
(in the plural) A woman's breasts. [from 20th c.]
Thus, it's been coined, yes, rather recently.
I suppose, with language changing, it is correct now to refer to "bosoms", although it isn't so, originally.
However, I must make the distinction in this case. "Bosoms" doesn't refer to one person's chest area, but rather the chest areas of several people in general, the way you would say, chins.