I recall hearing the idea that at least one of the gospels was written in Rome. If so, it seems strange to me that they would write it in Greek. So my question is: what fraction of authors in Rome wrote in Greek in the first half of the second century CE? Additionally, what fraction of readers in Rome could read Greek? What fraction of the population of Rome could read Latin? How did popular authors of the time get their work reproduced?
The upper classes of Rome were generally quite literate in Greek, however this is probably not entirely relevant to the question that prompted your question. Actually I cannot answer your direct question about percentages, but I can provide some data on the question that prompted your question.
What is relevant is that the Christian community in Rome operated in Greek for a considerable period of time. For instance, based on names, it may not have been until the late 2nd century that a Latin-speaking bishop came to office (Victor, ca. 189-198), and it was not until the 4th century that the liturgy in Rome was switched from Greek to Latin.
The gospel you are (probably) thinking of would presumably be Mark, based on its traditional association with the apostle Peter and the traditional location of Peter in Rome in the 60s shortly before his martyrdom.
Most of the Roman intelligentsia would have been bilingual -- politicians, writers, philosophers, and so on. In the eastern half of the empire, Greek was more common than Latin was -- remember that Alexander conquered the eastern Mediterranean several hundred years before the Romans did, and they had a lot of time to become Hellenized. There were even Greek colonies in southern Italy and Sicily that the Romans conquered. A lot of Roman culture was heavily influenced by Greek art, architecture, science, philosophy and literature.