In this sentence:
I don't fully understand the meaning of
I have found that
付一半 can mean "pay half", but
一人 confuses me (if it refers to one person, why is that form used instead of
一人 can be thought of as 'per person' or 'each person'.
This grammatical construction is extremely common in Chinese. I think it's called topical construction (correct me if I am wrong here). Essentially, you have the topic of the sentence (bus/taxi fare) at the start, followed by the subject, verb and the rest of the object.
So let's break it down:
I missed the last bit of your question the first time around. The measure word 个 is omitted. It means the same whether it's in there or not (in this case). However, 一人 in this sense is also used in some set phrases (such as 一人做事一人当 - one is responsible for one's own actions), and in those cases, you cannot use 一个人 in its stead. Fivesheep's answer has enough examples to give you a good idea how often it's used.