Apparently they stopped using the name Bludwine in the early 20s, so I assume it dates to the 1910s since it's ABM. And Bludwine was a brand of soda that was marketed to have some very questionable health benefits, hence the "for your health's sake" slogan.
You can still buy a soda called Cheerwine; ..I think produced in NC. Very tasty stuff. Might have been similar to the Bludwine. I have nearly the same bottle as yours but from Florida cities. 1915-1920 range.