The bubble packing method can generate high-quality node sets in simple and complex domains. However, its efficiency remains to be improved. This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation. Firstly, allow the viscosity coefficient c in the bubble governing equations to change according to the coordinates of the bubbles which are defined separately as odd and normal bubbles, and meanwhile with the saw-shape relationship with time or iterations. Then, in order to relieve the over crowded initial bubble placement, two coefficients $ω_1$ and $ω_2$ are introduced to modify the insertion criterion. The range of those two coefficients are discussed to be $ω_1$=1, $ω_2$∈[0.5,0.8]. Finally, a self-adaptive termination condition is logically set when the stable system equilibrium is achieved. Numerical examples illustrate that the computing cost can significantly decrease by roughly 80% via adopting various combination of proper schemes (except the uniform placement example), and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9. It shows that those strategies are efficient and can generate a node set with high quality.