No bus from JFK to Scarsdale.
Head to Manhattan and take Metro North to Scarsdale from Grand Central. You should have taken the 1 stop to HPN. It's not bad flying coach (once in a while).

FYI, I live near HPN. In the future, LGA would have been an easier airport to fly into. The express bus to 125th street and Lexington Ave drops you one block from the railroad station. It's about a 25 - 30 minute trip from 125th to Scarsdale. Total trip time is 60 minutes. I've done it before.
dh