In my experience, people absolutely do refer to the trains themselves as 新幹線. You're saying they don't?
Well, TGV can also be called bullet train in English, even though nobody in France says that - it's descriptive and everyone gets it. As Britannica puts it, "Inauguration of the line, just before the start of the Tokyo 1964 Olympic Games, was greeted by widespread international acclaim, and the Shinkansen was quickly dubbed the “bullet train” for the great speed the trains obtained and for the aerodynamic bullet shape of their noses." As for 新幹線、since people say 新幹線に乗る and 新幹線を降りる, in practical use the distinction between the train and the train network is pretty blurry.
新幹線
新幹線 does not mean "bullet train" as we call it in the West. Translating correctly as "new trunk line" actually refers to the network of lines themselves rather than the trains on which they run.