Jacquard fabrics have major bleeding problems. This kind of weave has a photo negative on the backside, which produces the bleeding. If jacquard is suspected, check the backside of the fabric by pulling up a skirt or looking at the inside of a cushion.
The presence of any kind of liquid can cause the colors to bleed through, so testing is crucial in this kind of fiber. Dry cleaning is the best for jacquard, but there is still a 50% chance of bleeding. Once bleeding has occurred on jacquard, there is no reversing it.