Inviscid bubble dynamics in a viscous fluid, moving with velocity $V$ far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. This dynamical system is well-posed (after a Tikhonov regularization) and possesses an extensive list of {} closed form solutions due to integrability. A new {} class of solutions is obtained and added to the {} class found earlier (Phys._Rev.E 89, 061003(R), 2014). The only attractor of the system selects the observable bubble shape and velocity $U=2V$ from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results essential for illustrating and understanding the most salient geometric aspects of the bubble dynamics are presented.