Hi there,
Yes - as the required the temporary visitor status is limited to 90 days, I'm afraid your girlfriend will not be eligible. There are not many alternatives for people who we not in Japan on tourism outside of the offers available to normal Japanese.
Assuming you'll want to travel together, discounted (5-10%) bullet train tickets can be purchased at the station or online if you book far enough in advance, or you can get around 5% off by purchasing her bullet train tickets from ticket vendors near mainline stations. She may also want to look into the Seishun 18-kippu although this cannot be used on bullet trains or limited express trains.
If you don't mind not travelling together, your girlfriend could look into discount flights or highway buses, although these are quite inconvenient compared to the bullet trains.
Hope this helps!