The rate at which colloidal particles can form biomolecular bonds controls the kinetics of applications such as particle-based biosensing, targeted drug delivery and directed colloidal assembly. Here we study how the reactivity of the particle surface depends on its molecular composition, quantified by the inter-particle rate of aggregation in an optomagnetic cluster experiment. Particles were functionalized with DNA or with proteins for specific binding, and with polyethylene glycol as a passive surface crowder. The data show that the inter-particle binding kinetics are dominated by specific interactions, which surprisingly can be tuned by the passive crowder molecules for both the DNA and the protein system. The experimental results are interpreted using model simulations, which show that the crowder-induced decrease of the particle surface reactivity can be described as a reduced reactivity of the specific binder molecules on the particle surface.