According to my understanding, you both got it right. The site I saw that on said there was a 2/3 chance of it being white, based on the number of possibilities of which marble (as opposed with bag) you chose, like so...
You chose the first marbe in bag A (second is white)
You chose the second marble in bag A (first is white)
You chose the white marble in bag B (other one is black)
They explained why it wasn't 50% by saying you were picking marbles, not bags, but the puzzle specifically says that you picked a bag.
Here's another one from the same site.
Three men are on safari and are ambushed by cannibals. The cannibals take them to their village and tie them to stakes, one behind the other, according to height. The shortes man is in back and he can see both men in front of him. The man in the middle can see only the man in front of him, but not the man behind him. The tallest man is in front and can't see either of the others. The cannibals then give them one chance to escape alive. The men are shown 5 hats, 2 of which are white and 3 of which are black. They are then blindfolded and a hat put on each. The extra two hats are hidden where none of the men can see them, then their blindfolds are removed. If one of them can say with absolute certainty what color his own hat is, they can all go free, otherwise they will all be eaten.
The man in back, who can see two hats, is asked what color his is and he answers "I don't know".
The second man, who can see only one hat, says "I don't know".
The tallest man, who can't see any hat, says "I know what color mine is".
What color was his hat and how did he know?
The TOG