Q. When washing for Shabes morning use, last night dishes with cold water can you use soap that creates bubbles?

A. Most Poskim maintain that there is no prohibition on creating soap bubbles when using an already properly diluted, cold soap and detergent solution, when needed for Shabbos use.
(Tzitz Eliezer 6, 34, B’er Moshe 8: 248, Shemiras Shabbos K. 14: 16, Eretz Zvi 70, Chaye Halevy 33) Vayaan Yosef argues that this should not be more stringent than pouring a glass of carbonated drink or beer that also produces bubbles.

See however, Shemiras Shabbos K. (16: 30) in Horav S.Z. Auerbachs Zt”l name, that when the intention is indeed to make bubbles, as with a children’s bubble making soap solution, it should be on the onset avoided, but you do not have to stop the children when they do so.
Horav Shlomo Miller’s Shlit’a opinion is that it is permitted to use the above-described dish washing solution when needed.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a