Molecular bottlebrushes have attracted attention for applications in molecular medicine as drug delivery vehicles. Their very low critical micelle concentration and the variety of different nanostructures they can form in solution makes them ideal molecular constructs for those applications. To date, however, little is known about the effect of the architectural parameters on the bottlebrush solution self-assembly and its response to the presence of hydrophobic solutes. In this work, we have performed extensive numerical simulations to elucidate the role of side-chain size-asymmetry and bottlebrush molecular weight in the morphology of unimolecular particles in aqueous solutions. In addition, we have investigated the synergistic effects of adding hydrophobic solutes into the polymer solution. Our simulation results show that a continuous cylinder-tosphere morphological transition takes place as the concentration of hydrophobic solutes increases. Importantly, our simulation results suggest that the total hydrophobic content is the parameter driving the morphological transition, when this quantity reaches a value in the ranges 0.6 and 0.7, then the nanoparticle transforms into a spherical object. Our results agree qualitatively with previous experimental results and provide guidelines for the molecular design of bottlebrushes that target specific morphologies for diverse applications.