Dynamic properties of bubble domains at low drive pulse field are examined by the bubble transport method. Important findings are as follows. 1) The bubble does not move unless the pulse duration exceeds a critical value which depends on the pulse amplitude. 2) A minimum pulse amplitude is also required for the bubble translation which depends on the pulse duration. 3) As the pulse duration goes to infinity, the minimum drive field approaches a constant value which is different from the dynamic coercivity. 4) As soon as the pulse duration exceeds the critical value, the bubble is displaced discontinuously by a finite distance independent of the drive field. All of these properties are adequately explained by a simple phenomenological theory, in which the domain wall is assumed to be connected by springs to pinning sites until the wall is displaced by a finite distance.