you can use optical density or direct plating method to evaluate bacteria amount in liquid medium. When you get the growth curve, you can pick up starting and final points during the exponential growth, and find average time for 2-folds difference of bacteria number. But it will be true for this experiment only.
What sort of analysis are you thinking of - and why?
Bacterial growth is affected by anything - temperature, nutrient levels, pH, age of population, genus, species, variety etc., etc. Any population of bacteria will be heterogeneous and you can determine only the mean generation time unless you watch a single cell under a microscope but many bacteria produce extracellular growth regulators (antibiotics) that probably affect their own growth rate. The times taken for a population of bacillus spores to germinate follows a Weibull distribution in which YT, the fraction gemnated in time T, is given by YT = exp(-BT-R). R defines the shape and B the scale. Experimental results suggest that R=2, which gives an asymmetric shape and a Rayleigh distribution.
I suspect hat most functions of most bacteria have a similar dsitribution.