Which bulges are favoured by barred S0 galaxies?

S0 galaxies are known to host classical bulges with a broad range of size and mass, while some such S0s are barred and some not. The origin of the bars has remained as a long-standing problem -- what made bar formation possible in certain S0s? By analysing a large sample of S0s with classical bulges observed by the Spitzer space telescope, we find that most of our barred S0s host comparatively low-mass classical bulges, typically with bulge-to-total ratio ($B/T$) less than $0.5$; whereas S0s with more massive classical bulges than these do not host any bar. Furthermore, we find that amongst the barred S0s, there is a trend for the longer and massive bars to be associated with comparatively bigger and massive classical bulges -- possibly suggesting bar growth being facilitated by these classical bulges. In addition, we find that the bulge effective radius is always less than the bar effective radius --indicating an interesting synergy between the host classical bulge and bars being maintained while bar growth occurred in these S0s.