You could use other benzophenones instead.
Benzophenone-3 shouldn’t be a problem because it’s use in hand washes and photosensitisation won’t be an issue. It’s unfortunately commonly regarded as ‘bad’.
Benzophenone-5 is the sodium salt of BP-4.
Use a different sunscreen UVA filter such as diethylamino hydroxybenzoyl hexyl benzoate, butyl methoxydibenzoylmethane, or bemotrizinol.
Try ferulic acid: It doesn’t absorb as good in the UVA range and is less stable than common UV filters but it’s natural.
Use a different bottle material which is less transparent for UVA (polycarbonate, polystylrol, or plastics with additives).
Try without any BP-4 and see if you still get photobleaching.
Use chemical protection such metabisulfite.