How many BC years are there?

Answer 1

As many as there are useful. The BC indicates the years before the Christian Era. For recorded human history that could go back as far as 8000 to 9000 years BC. Any further could not be very accurate therefore not be very useful.

Answer2:

Approximately 4.55 billion years. Just because humans weren't recording it, doesn't mean we can't determine it. Radiometric dating suggests 4.55 billion years since the formation of the Earth. Though this is the time from when the Earth was formed. If you want the total time since the universe was formed, it is approximately 13.75 billion years.