Re-calculating the years, using the Gregorian years, from 0 A.D to 2010, What year would we find our selves in?

As the quote says, there was no such year as "0 AD". The year that followed 1 BC was 1 AD. Or as we'd say it in modern terms: the year 1 BCE was followed by the year 1 CE. So are you asking how many actual solar years have ped since 46 BCE?