I believe that it was a collection, anyway.
It was from the early to mid 90s and one of the stories involved a woman staying at a cabin during a dark and stormy night. A green sphere appears (or maybe crashes?) and the woman is very afraid of it. After a time skip, however, they become good friends reminiscing about their first encounter. I believe they also met with other aliens at some point.The green sphere acts as a mentor for the woman, who works as an agent for an interstellar organization. It might have been the first in a series of short stories.
The second story involved a student exchange program between an alien species (looking like green Big Birds) and humans. They have just initiated first contact, and the narrator only learns that she is part of the program after going back to her dorm (she's a college student) and finding her new alien roommate in a towel after taking a shower. Both species want to make a good first impression, but the alien species is far more communal than humans normally are.