I have never actually noticed the wording on the website, I had just assumed that it would be valid on the U18 (never had to use one in Bath as I had a bus pass for the year anyway). So can't answer about that bus.
But the 18 is pretty frequent anyway, even during university holidays.
So even if the plusbus ticket does not include the U18, then it wouldn't matter too much.
In terms of the 8, I am not even sure if First even run that anymore. I seem to remember posters saying that it is being withdrawn (and think Ivo mentioned on this forum that it is being withdrawn too). Even if they do still run it, it is a university term only service and even then was very limited in terms of times. So I would just say forget this service.
The 20 that is mentioned in previous posts, run by wessex connect, does go to the university, but its the Bath Circular so takes a pretty long route. Nots really worth it unless you fancy a tour of random parts of the city!
Just as a bit of a help, if you are going straight to the university from the railway station, the bus stop is very close. Just opposite the bus station (and the bus station is right next to the train station).
(ps - I have just graduated from Bath, so if you / your daughter have any quick questions, feel free to send me a PM).