A shampoo or soap containing bay cannot be assessed from the plant name alone. The full formula, intended use and evaluation of the finished product matter.
Cosmetic purpose differs from treatment
Cleansing or adding fragrance is different from claiming to treat eczema or stop hair loss. FDA explains that aromatherapy products are assessed according to intended use; an ingredient name does not establish therapeutic efficacy.
Source: FDA — aromatherapy products
Concentrated homemade applications
A study of leaves does not establish the safety of an oil applied to skin. Essential oils can cause skin reactions, and natural does not mean harmless. Follow finished-product instructions and do not use mixtures of unspecified concentration as treatment.
Source: Poison Control — essential oils
A checklist for manufacturers and buyers
Specify whether you need leaf essential oil, fruit oil or a finished cosmetic. Record ingredient name, plant part, batch identity, required safety documents and role in the formula. Raw-material documents do not automatically establish every use condition or the finished product’s efficacy.