Thank you for your help.
What is the proper disposal of plastic kiddush cups and plastic plates used to hold bread during Shabbat?
You can throw them both out in the garbage and there is no need to do anything special with them. Although it is preferred not to throw out mitzva items in a degrading way, such as in the garbage, this only applies to mitzva items that are evident that it is was used for a mitzva. However regular items such as a regular plastic cup that was used for kiddush, a shovel used to bury someone, or a box that was used as a pushka, do not have to be disposed of respectfully as the fact that it was used used for a mitzva is not evident on it. Therefore they can be thrown out in a normal fashion.
A plate that holds the bread on shabbos is even less than this since no mitzva was performed using the plate.
Ginzei Hakodesh 20-5,6