I was a lot younger, a teenager actually, and my dad took the family to a glass blowing facility. It was interesting watching them blow the glass into something, anything. The way they blow and turn the tube to get different shapes was amazing.
This article (http://www.thehistoryblog.com/archives/62449) about an ancient tomb discovered on the Greek island of Euboea is interesting, but for this thread on ancient glass bottles I thought it was specifically interesting to see some from about 2500 BC. I took the picture from the article.
If you check your largest local city, my guess is that you will find a glass studio that offers classes where you can do this. The studio we have locally will run specials on Groupon. I think a one-hour session is $125, and that includes instruction and the blowing of one piece. My wife has purchased for me two sessions over the years. It’s great fun.