Recently they reported the average time to get infected after connecting an unpatched XP machine to the internet dropped from 16 minutes down to 12 minutes (
Slashdot), though in reality the time you'd experience would be much lower.
Note that the Sasser virus isn't the only one that used the exploit in lsass.exe. Since it was made public thousands of botnets use that exploit to spread, so being infected via that exploit doesn't necessarily mean you got the Sasser virus. You could have any.