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The problem of a single acoustically driven bubble translating unsteadily in a fluid is considered. The investigation of the translation equation allows for identifying the inverse Reynolds number as small perturbation parameter. The objective is to obtain a closed-form, leading order solution for the translation of the bubble, assuming nonlinear radial oscillations and a pressure field as the forcing term. The result is the ability to predict and explicitly understand the rapid and slow transients of bubble displacement, which is proportional to the average acoustic radiation force. The periodic attractor of the Raleigh-Plesset equation serves as basis for an optimal acoustic forcing designed to achieve maximized bubble translation over one dimensionless period. At moderate acoustic intensity, maximizing the radial variance, thereby enhancing bubble collapse, leads to displacement many times larger than the case of purely sinusoidal forcing. The survey covers a wide spectrum of driving ratios and bubble diameters physically relevant to biomedical applications. Shape stability issues are considered. Together, these results suggest new ways to predict some of the direct and indirect effects of the acoustic radiation force in biomedical applications: e.g., targeted drug delivery, selective bubble driving and accumulation. [Work supported by NASA Microgravity Fluid Physics Program.]