Thankfully, it's very easy to make a lamp out of a wine bottle. They sell lamp fixtures attached to corks, and you just pop them right in! I didn't have to pay for the wine bottle, it was a hostess gift from my niece to my sister-in-law, and she gave it to me when I said I'd make a lamp. The kit and the shade were $58 total, but I got them for free because I paid with reward points from my credit card.
Since I took this photo, we added a vinyl record to the top so it's not bright when you look down. That also makes a nice halo of light on the ceiling instead of a huge bright spot.
They also make cool ones that shine a light down into the bottle. Wasn't what I was looking for for this project, but they're neat!
I did indeed get the fixture on Amazon. It's this one. I also had to get this thing and am glad I thought of it while I was ordering the shade and the fixture.
I do most of my shopping on Amazon tbh. It's really frustrating to drive around and not find what I want.