Globular proteins do not have a CMC like surfactant, but have hydrophobic regions in which hydrocarbons can be solubilized. Serum albumin has 18–20 hydrophobic regions. The lysozyme globule has only one hydrophobic region. The thermodynamic parameters of the solubilization of hydrocarbons are similar to the solubilization of surfactants. Literature: Izmailova V.N., Rebinder P.A. Structure formation in protein systems. Moscow, Science, 1974. ( Rus)
I did not work on loading drugs in nanoparticles. I am working on adsorption of proteins on the nanoparticle surface
Anyway, I remember for releasing a drug we should determine the pH, salinity and temperature of the media. If the affinity of BSA into your nanocarrier is high you should change the carrier.