Bullock cancelled an appearance at the London premiere of her movie "The Blind Side" saying she couldn't attend for "unforeseen personal reasons."
James told People magazine he exhibited "poor judgment" and said, "I deserve everything bad that is coming my way."
If Bullock and James split, it continues a long chain of broken relationships for best actress winners.
Among them, Halle Berry, Reese Witherspoon and Julia Roberts, who all split from their partners within a year of winning. Hillary Swank and Charlize Theron are also on the list.
And in recent weeks, past winners Susan Sarandon and Kate Winslet have separated from their mates.