It has recently been shown that the behaviour of a gas bubble in a uniaxial straining flow can be used as a simplified model to describe some important aspects of the more complex, turbulent bubble break-up problem, provided that the Reynolds and the Weber numbers are sufficiently large. In the present investigation, we extend that work and, using a level-set numerical scheme, we analyse the influence of the bubble Reynolds number on break-up time, $t_b$, for supercritical Weber numbers, $\hbox{\it We}\,{>}\,\hbox{\it We}_c$, where $\hbox{\it We}_c$ is the critical Weber number. It is observed that the viscosity introduces corrections of ${{O}}(1/\hbox{\it Re})$ in the break-up time obtained in the limit $\hbox{\it Re}\to \infty$. In addition, the action of other possible mechanisms of break-up at subcritical Weber numbers, $\hbox{\it We}\,{<}\,\hbox{\it We}_c$, is also explored.