Bottlebrush polymers, formed from a linear backbone polymer with a high density of grafted side chains, are functional macromolecules useful in molecular assembly and responsive materials due to their unique physical properties. Interactions between the side chains stiffen the molecular backbone and imbue it with a molecular dimension beyond simply the polymer length, drastically altering dynamic relaxation and intrapolymer interactions. Simulation prediction of these material properties remains a challenge, however, because they specifically depend on side chain degrees of freedom that are computationally expensive to model. In this work, we use the wormlike cylinder framework to systematically map molecular features from a single-molecule hybrid Brownian dynamics and Monte Carlo (BD/MC) simulation with explicit side chains to a simple touched-bead polymer model. We use static properties from the explicit side chain simulations such as end-to-end distance and radius of gyration to parameterize the wormlike cylinder model and consistently reproduce other single-chain properties such as hydrodynamic radius and intrinsic viscosity. This parameterization yields the stiffness parameter and equivalent diameter of a bottlebrush and is compared to prior scaling theories and simulation results. We find that the wormlike cylinder model, appropriately parameterized, provides an accurate description of these quantities over a wide range of side chain lengths and grafting densities. We demonstrate that a coarse-grained representation is able to consistently reproduce the bottlebrush structure and show that the wormlike cylinder model can be useful for large-scale coarse-grained simulations of bottlebrush suspensions.