The asphalt rubber blend properties are strongly related to its base components properties. The base bitumen composition is considered as a key factor influencing the final rheological properties of asphalt rubber binder. This paper describes results from a laboratory investigation of the interaction between crumb rubber and different composition bitumen according to the wet process. The bitumen composition is determined according to the SARA decomposition approach. The composition’s analyses are carried out on both base bitumen and residual bitumen extracted from the final asphalt rubber blend. The extraction process consists of a centrifuging procedure ensuring a reasonable aging and a minimum physical or chemical alteration of the phases. The evolution of the bitumen composition during the curing process indicates that aromatic fractions of bitumen are the major cause of rubber swelling through a migration phenomenon. Viscoelastic properties measurements demonstrate that base bitumen composition should be selected carefully to achieve a good compromise between a sufficient rubber swelling and a reasonable viscosity of the final binder.