You can get logarithmic growth of E.coli within 12 h by inoculation of actively growing young cells around 1% v/v (3 log ) in Either BHI or LB broths and by incubation at 37 degrees at pH 7.4 and moderate chaking conditions.
for addition, also we should consider about plasmid antibiotics ( selectable marker ) because most probably you have your target plasmid with specific selectable marker in E. coli, if your antibiotic is Amp the optimize time is around 12 hr, and more then that it can make problem because Amp, it can broke in LB after 12 hr, for Kan should be around 12 10 14 hr. 37 degree and shaking of 150-250 rpm.