While the dynamics of dust transport around an airless body has been a focused area of research in recent years, various challenging aspects still remain to be addressed for small asteroids where the dust dynamics is determined by the competing effects from gravitational force, electromagnetic force, and solar radiation pressure. This paper presents an investigation of dust transport and distribution around small asteroids utilizing numerical models and laboratory experiments. This investigation includes the following studies: 1) 3-dimensional fully kinetic Particle-in-Cell (PIC) simulations of plasma flow past an asteroid to determine the electric field around the asteroid and calculate surface charging. The PIC model utilizes an immersed-finite-element based field solver which is capable of resolving realistically shaped asteroid and calculating the surface potential self-consistently from charge deposition. 2) Gravitational field modeling for a realistically shaped asteroid. 3) Laboratory measurements of dust grain charging on asteroid surface in a simulated near asteroid plasma environment. 4) Dust transport simulations which incorporate the results of the PIC and gravitational field model and dust charging measurements. Simulation results are presented for the following 2 scenarios: a) electrostatically levitated dust grains and b) impact ejection of dust grains. We find that local electrostatic fields strongly influence the trajectory of charge dust grains near surface, while local gravity fields may determine distributions at further distances. We discuss the effects of asteroid composition, grain size and space plasma environments on dust levitation and transport. Implications of the study may advance the current understanding the asteroid environment and improve functionality of future spacecraft design for asteroid rendezvous mission.