Here is my cheapo blender (purchased for using only with dye) and a typical canning jar. (Note: the wide mouth ones don't work--just the standard Bell/Kerr ones do.)
Here's the blender base assembly taken apart. There's usually a blade part, a rubber washer that fits on the blade (see the grey thing) and the blade base that screws onto the blender pitcher.
The blade sits in the screw-on base, like this:
Now, that whole part screws onto the jar, like this:
If you were mixing dye, you would have put the dye powder and water into the jar and then put the blade/screw on base on TOP of the jar, like you were screwing the jar's lid on. Be sure to check that the blade/base is screwed tightly onto the jar, that it's threaded correctly...because you're going to turn it upside down and you don't want any leaks.
Voila! Mix away... then, take the blade/base off of the jar, put the original jar's lid on the jar, and you can store the dye in the jar and mix more dye in other jars. I bought a case of 12 quart-sized jars at the hardware store for $8. They have smaller jars, too. And I'm told you can find these at yard sales for way cheap.