One could speculate that after the 2nd capful, it would not matter how much water your tub holds, it would not be enough to dilute the concentration of chemicals effectively to avoid a health hazard. One would also expect that a shallow bath is more likely to generate more bubbles because the soap is not as diluted. In any event, follow the directions given by the manufacture on the label. When preparing the bath, thoroughly mix the bubble bath with the water before letting your child enter the tub. Adult supervision is always a must.
Soap is slippery stuff.
If the product does not produce the bubbles or the bubbles do not seem to last before the child enters the tub and you suspect the product is not working as advertised, drain the water, draw a new bath and later return the defective product. If the product is defective, adding more is not likely to improve product performance. In the Speakout column, J. Robert Ashley from Tampa, Florida wrote a very informing commentary. Apparently 2 decades of magnetic field research has not yet explained why living near overhead power lines increases the risk of childhood leukemia. His research has lead him to the conclusion that studies should have been measuring electric fields instead.