I believe your example to be a very nice fake. Below is my reasoning from empirical observations in my study of ancient and medieval glass including how fakes are produced. The market for fakes has existed for over 100 years, but it really ramped up in the 1970s.
The bottle's handles and applied strings are rather perfect. Two for a penny was the worth of glass at the end of the Roman empire-- glass's heyday. They seldom perfected pieces. Rather, they just made them look good. There is also too much of a satin sheen left on it even though the whole bottle has been given a weathered appearance by a dip in acid. While one of my Byzantine examples still has much of its original glossy surface layer left, other layers are weathered due to the silicates in the glass being mixed irregularly throughout it. Perfectly uniform deterioration is a red flag, especially when it just looks rough and is of a single color. I bought a cobalt example like yours at a museum gift shop once differing only in its lack of weathering. It was blown in Egypt.
While pontils are near ancient, they tend not to be seen on Roman glass. They are seen on medieval Near and Middle Eastern glass dating to the 500s C.E. and newer. The Eastern bottles, though, are thicker/heavier and more naturally translucent rather than clear. Very crude. As such, this example cannot be Levantine in origin, either.
Ancient weathering looks like this: https://d3h6k4kfl8m9p0.cloudfront.net/stories/jtJ92JKuDNphrSmkqbjNZA.jpeg https://d3h6k4kfl8m9p0.cloudfront.net/stories/hLxhOLqhjD7-YU6QRAZoeg.jpeg
The above links are of multiple types of genuine weathering on a single early medieval example of glass. Any of those types is typical: Enamel-like, iridescent, or both.
Thanks for your info. i'm still left wondering about this one, but leaning towards fake, the one example you found has a design like mine, but differs a lot in patina and delicacy. Also, the beautiful iridescent patina seen on many genuine examples of ancient glass is mostly absent on others, due i'm sure to conditions of where it was found, bottom of an ocean or buried in a desert. Probably fake, but still would love to have an expert actually look at it.