The formation of a polymer-surfactant complex has been studied in bulk solution using dissipative particle dynamics simulation of a system containing polymer, surfactant, and water. Widom insertion is used to obtain the surfactant chemical potential. Two distinct modes of surfactant adsorption on the polymer have been observed, depending on the interaction mechanism. These are (a) continuous adsorption and (b) polymer-surfactant aggregation via discrete micelles. If the binding between polymer and surfactant is dominated by hydrophobic interaction (i.e., when the surfactant tails tend to adsorb on the polymer), continuous adsorption is found, leading to molecular bottlebrush or swollen cage conformations. If the binding between polymer and surfactant is dominated by the surfactant headgroups, micellar adsorption is found, leading to a necklace of micelles on a polymer backbone. For each interaction strength between polymer and surfactant headgroup, there is an interaction between polymer and surfactant tail where the mode of adsorption crosses over from micelle adsorption to molecular bottlebrush conformations. This crossover is comparable to a critical point in the condensation of gases to liquids. A schematic phase diagram indicating where the various adsorption modes occur is given. The polymer endpoint separation as well as its swelling exponent are found to pass through a minimum as the surfactant concentration is increased. When the bulk critical micelle concentration is reached, the polymer swells beyond its original size.