To become a professor of actuarial science, should I pursue graduate school immediately after B.S. or get some professional experience first?
The work experience would be helpful in an academic career. But it doesn't have to be one decade. More like one to two years. 

Many people stay with accounting firms for 1-2 years just to get their CPA. You could benefit from the ASA. So stick around long enough to get it, then start looking to leave when you do.