This recipe is far too vague to be useful, by calling for "powdered detergent", since "detergent" is just a word for "cleaner", and the only further specification is that it not be soap. There was a time, generations ago, when the word "detergent" was understood almost exclusively to mean a high-suds all-purpose or light-duty powder, and at that time, most of those were good as the basis for a bubble bath, although dissolving them in and glycerin for storage would not have been as good an idea as simply throwing those 2 Tbsp of powder directly into the bath. Nowadays those products, even the ones sold under the same brand name as ~70 years ago such as Dreft, are unsuitable for this purpose, and most of the other things one might have have around the house as "powdered detergent not soap" range from unsuitable to downright harmful in such an application.