1 BC should be renamed year 0. Then the years 0-99 are the 0th century, the years 1900-1999 are the 19th century, etc.
To avoid confusion between new style and old style centuries, create a new word, "centan", meaning "100 years" and use cardinal instead of ordinal numbers, for conciseness. Then the years 1900-1999 are the 19-centan.
1 BC should be renamed year 0. Then the years 0-99 are the 0th century, the years 1900-1999 are the 19th century, etc.
To avoid confusion between new style and old style centuries, create a new word, "centan", meaning "100 years" and use cardinal instead of ordinal numbers, for conciseness. Then the years 1900-1999 are the 19-centan.