Translation:I bought a bullet train ticket.
When speaking to people in Japan or who have been to Japan I hear shinkansen usually. But when I talk to most other people I have to say bullet train to be understood.
Shinkansen is a specific set of bullet train lines, but since it's pretty much the only set that the Japanese will get to know unless a new set is made in Japan with a new name, its name is synonymous with bullet train in their culture.
I would assume it's like saying the Tube to someone who's unfamiliar with London.
For those really curious the original Shinkansen was called "chotokkyuu" 超特急 for "Super Limited Express". This was to distinguish it from the then fastest trains (and still operating on some lines) "tokkyuu" 特急 Limited (Special/Exclusive) Express. This name "Super Express" is still used in English announcements. "Bullet Train" is only a nickname that became popular from documentaries and has never officially been used in Japan.
The term bullet train (Japanese: 弾丸列車 Hepburn: dangan ressha) originates from 1939, and was the initial name given to the Shinkansen project in its earliest planning stages.
Shinsaku Matsuyama (2015). 鉄道の「鉄」学: 車両と軌道を支える金属材料のお話 [Iron for Iron Horses: The Story of the Metals Used in Rolling Stock and Railway Tracks]. Tokyo: Ohmsha Ltd. ISBN 9784274217630
Having travelled in Japan, shinkansen is more natural for me. The Japanese never call it bullet train, even when speaking English so I'm glad they support transliteration on this one.
Duolingo needs to add pictures for some words. Bullet train, police box, Post office.. they're easily forgettable.