The sensitivity and efficiency in contrast-enhanced ultrasound imaging and therapy can potentially be increased by the use of resonant monodisperse bubbles. However, bubbles of the same size may respond differently to ultrasound due to differences in their phospholipid shell. In an acoustic bubble sorting chip, resonant bubbles can be separated from the polydisperse agent. Here, a sample of acoustically sorted bubbles is characterized by measuring scattering and attenuation simultaneously using narrowband acoustic pulses at peak negative pressures of 10, 25, and 50 kPa over a 0.7-5.5 MHz frequency range. A second sample is characterized by attenuation measurements at acoustic pressures ranging from 5 to 75 kPa in steps of 2.5 kPa. Scattering and attenuation coefficients were modeled by integration over the pressure and frequency dependent response of all bubbles located within the non-uniform acoustic characterization beam. For all driving pressures and frequencies employed here, the coefficients could be modeled using a single and unique set of shell parameters confirming that acoustically sorted bubbles provide a uniform acoustic response. Moreover, it is shown that it is crucial to include the pressure distribution of the acoustic characterization beam in the modeling to accurately determine shell parameters of non-linearly oscillating bubbles.