“bi-” is from Latin and “di-” is from Greek. “uni-” and “mono-” are another such pair. Often the choice between them is dictated by the origins of the other elements of the word.
At the time, pedants loudly denounced words that were created out of a mix of Greek and Latin roots. Alternative words were often introduced, but they didn’t win out because they usually didn’t sound as good.
Here’s an example I happen to have sitting by my hand. From Oona* Strathern,* A Brief History of the Future*:
Oosip* Flechtheim invented both the science of and the word futurology. He faced an “objection from an English philosopher who said it was doomed to fail because the term, like the word sociology, combined both Latin and Greek word roots (the same misguided and pedantic argument was also once used about the word ‘television’).” The philosopher wanted to use the term “mellontologie.”
Formal British education throughout the 19th and well into the 20th century mandated the study of both Greek and Latin. (American private schools mostly copied this slavishly.) It was the hallmark of a gentleman and someone who was well educated, which were intended to be synonymous. Mixing Latin and Greek was a barbarism, showing that one was neither. Unfortunately for them, by the 20th century the lead in invention and therefore in naming had passed over to Americans who didn’t have this heritage and were barbarians in this sense, since they cared not a whit about mixing Latin and Greek. (Despite the name Flechtheim was American.) This has been true ever since.
It’s a matter of personal taste. Personally, I tend to prefer coined words that don’t mix Latin and Greek because I think they sound better, but I don’t reject or avoid well-established words that do mix them, like “automobile” or “television”.