Well, it was more likely in the BC range, but yeah, would be year 0 instead.

Year 0 doesn't exist either. 1 BC is directly followed by 1 AD

Year 0 is obviously in the middle of the two.

Here you go: https://en.wikipedia.org/wiki/Year_zero

Because zero wasn't invented until much later.

Hmm, I don't think so: https://www.scientificamerican.com/article/what-is-the-origi...

Also, AD / BC wasn't devised until 525 AD, and zero was common at that point, so that can't be the reason: https://en.wikipedia.org/wiki/Anno_Domini

EDIT: Apparently I'm wrong :)

Neither the concept nor a symbol for zero existed in the system of Roman numerals. The Babylonian system of the BC era had used the idea of "nothingness" without considering it a number, and the Romans enumerated in much the same way. Wherever a modern zero would have been used, Bede and Dionysius Exiguus did use Latin number words, or the word nulla (meaning "nothing") alongside Roman numerals.[1][3][4] Zero was invented in India in the sixth century, and was either transferred or reinvented by the Arabs by about the eighth century. The Arabic numeral for zero (0) did not enter Europe until the thirteenth century. Even then, it was known only to very few, and only entered widespread use in Europe by the seventeenth century.

https://en.wikipedia.org/wiki/Year_zero

Forgot the sarcasm flag in that post..