Parah 9:6

One may not carry sanctification water or the ashes of the red heifer across a river on a ship, nor may they be floated on the water, nor may one stand on one side of the river and throw them to the other side. One may, however, cross the river (by foot) even with the water up to his neck (which resembles floating them). One who is ritually clean for the sanctification may cross a river (in a boat) holding an empty, ritually clean vessel for the water, or water that has not yet been sanctified.

Parah 9:7

If the ashes of the red heifer got mixed with regular ashes, we follow the majority when it comes to rendering people unclean but the ashes may not be mixed in the sanctification water. Rabbi Eliezer says that all the ashes may be mixed in the sanctification water (because the cow’s ashes are certainly in the mixture).