In champagne and carbonated beverages, bubble nucleation was mostly found to take place from tiny Taylor-like bubbles trapped inside immersed cellulose fibers stuck on the glass wall. The present paper complements a previous paper about the thorough examination of the bubble nucleation process in a flute poured with champagne (Liger-Belair et al. J. Phys. Chem. B 2005, 109, 14573). In this previous paper, a model was built that accurately reproduces the dynamics of these tiny Taylor-like bubbles that grow inside the fiber's lumen by diffusion of CO2-dissolved molecules. In the present paper, by use of the model recently developed, the frequency of bubble formation from cellulose fibers is accessed and linked with various liquid and fiber parameters, namely, the concentration c(L) of CO2-dissolved molecules, the liquid temperature theta, its viscosity eta, the ambient pressure P, the course of the gas pocket growing trapped inside the fiber's lumen before releasing a bubble, and the radius r of the fiber's lumen. The relative influence of the latter parameters on the bubbling frequency is discussed and supported with recent experimental observations and data.