In practical usage, Bte as a conjunction is used tremendously often. As toritobe san says, in many cases you can infer (or imply, when you're the speaker) cause/reason. Note that Bte form for adjectives is used like this as well.
kagi ga hairanakute, komatta (the key wouldn't go in, so I had trouble [getting in]) ... verb case (hairu)
hon ga furukute, peeji ga hirakanai (the book is old, so I the pages won't open) ... adjective case (furui)
As you get more familiar in real-world situations, you can even leave off the second part after Bte in the conversation:
Doushite okureta no? (why were you late?)
Sumimasen. Takushidai ga nakute... (Sorry. I didn't have cab fare, so...[inferring that you walked or found some other way to get there])
Next, item:
You said:
高校で二年間日本語を勉強して大学に入ったばかりのキャロル・ベーカーが、日本会のパーティーで日本語の石山先生に初めて会う。
Carol Baker, who studied Japanese for two years in high school and just entered university, meets Japanese professor Ishiyama for the first time at a Japanese company party.
Sounds like from the context that Carol is still a U student...assuming 日本会のパーティー isn't a typo...then Nihonkai = Japan Club (the school's club)?
If, some day, you want to become a standout translator, think about your translated product a bit more. Aside from "nihonkai," your translation is technically correct. As a matter of fact, nine out of ten translators would write it just the way you did. Well, maybe eight out of ten. The other two would go one step further and attempt to put "translated English" into more natural English. Something like the following [from the context...this is setting up a conversation that will take place between Carol and the professor, right?]
"Carol Baker just entered university [the name of the U would be better] after two years of high school Japanese. She is meeting Professor Ishiyama for the first time at a party sponsored by the school's Japan Club. Professor Ishiyama is a professor of Japanese at the university."
Of course, there are all kinds of ways to write that, depending on your preferred style.
"Carol has just enrolled in the university after taking two years of Japanese in high school. She is meeting Professor Ishiyama, a professor of Japanese, for the first time at a party sponsored by the university's Japan Club." [you could even switch the order of these two sentences to talk about the party first and then the conditions of Carol's enrollment in school]
Which is better?
Who's to say? I like the first one (three sentences). Some would prefer the second version. Some will prefer your version, because it's easier to track from the original (more of a direct translation).
Sorry for getting all philosophical...just a pet topic of mine.