This work studies the link between the bursting process of a flat plate laminar separation bubble and the modification of the stability characteristics of the separated shear layer due to changes in the flow parameters. A vast population of short and long laminar separation bubbles was surveyed by means of Particle Image Velocimetry instrumentation for different values of the Reynolds number, the free-stream turbulence intensity and the streamwise pressure gradient. A fine-step variation of the free-stream velocity allowed us to determine the critical Reynolds number at which bursting occurs. Successively, the most amplified wavelength and frequency were computed for both the short and the long bubble regimes. Once scaled with the boundary layer displacement thickness at separation, the average wavenumber of the vortices shed by the bubble was found to be constant and equal to about 0.9 in the short regime, accordingly to previous studies. Differently, this quantity reduces to about 0.6 in the long bubble regime, and a marked change in the Strouhal number of vortex shedding occurs. Also, the temporal growth of spanwise vortices was seen to occur in the recirculation region of long type bubbles, being linked to an absolute instability of disturbances. The currently acquired data demonstrate the existing link between the bursting process of a laminar separation bubble and a marked change in the instability mechanisms driving the transition process of the boundary layer. A simplified correlation for the prediction of bursting is provided in this work as a function of the free-stream turbulence intensity and the streamwise pressure gradient.