The second harmonic radiation of acoustically driven bubbles is a useful discriminant for their presence in clinical ultrasound applications. It is useful because the scatter from a bubble at a frequency different from the driving can have a contrast-to-tissue ratio better than at the drive frequency. In this work a technique is developed to optimize the scattering from a microbubble at a frequency different from the driving. This is accomplished by adjusting the relative phase and amplitudes of the components of a dual-frequency incident ultrasound wave form. The investigation is focused primarily on the example of dual-mode driving at frequencies of 1 MHz and 3 MHz, with the scattering optimized at 2 MHz. Bubble radii of primary interest are 0.5 to 2 μm and driving amplitudes to 0.5 atm. Bubbles in this size range are sensitive to modulation of driving. It is shown that an optimal forcing scheme can increase the target response eightfold or more. This suggests new applications in imaging and in bubble detection.