Because BSA has three SH group on the surface of its tertiary structure, BSA can covalently bind to Au nanoparticles directly.
If thiol-ending linker is used, the situation is more complicated since there are two types of bound BSA: binding via linker and direct binding. Nevertheless, very high density of the linker can maybe inhibit the direct binding due to steric effect.
You should be able to modulate the adsorption density by simply controlling the adsorption isotherm....i.e., modulate the concentration of BSA in solution to obtain different coverage amounts. Then remove excess BSA by mild centrifugation with replacement of the supernatant.
BSA is easily taken up by citrate capped AuNPs, and since they both carry a net negative charge, there will be no problems with electrostatic screening/aggregation of partially charged particles. The BSA "sticks" to Au very well. It's not clear if this is due to the single free external SH group at Cyst-34 (in the "normal" form of BSA) or other bonding mechanisms. Another person mentioned there are 3 free external SH groups on BSA. I do not believe this to be correct. Our paper on BSA uptake by AuNPs has the relevant citations and information (dx.doi.org/10.1021/la104124d | Langmuir 2011, 27, 2464–2477). Proteins, in general, are readily taken up by Au.
One last thought...you can also modulate (somewhat) the adsorption density by adjusting the pH. The paper I mentioned above also discusses the effect of pH.
If you like to stay with citrate capped Au nanoparticles it is not that easy to bind BSA,
when citrate moieties are bound on the Au nanoparticle surface in huge amount (really ?):
BSA has an isoelectrical point of around 4.5 meaning, that at pH=7 it has a negative net charge. Hence, if you like to bind BSA electrostatically, you have to use a buffer, which presents a pH value of around 3-3.5. Then BSA has a positive net charge.
In your case, why not try to use citric acid solution (pH= ca. 3) as the buffer system for BSA.
Just dissolve your Au nanoparticles in 0.001 m citric acid (first look, if this suspension is still colloidally stable) and then add BSA (0.01 M to 0.001m) in 0.001M citric acid in small portions and check colloidal stability.