We study the properties of bars in a series of zoom cosmological simulations (Martig et al.2012, Kraljic et al.2012). We find that bars are almost absent from galaxies at z>1, and if they form they tend to be quickly destroyed by mergers and instabilities. On the contrary, at z<1 bars are long-lived, and the fraction of barred galaxies rises steadily. Bars are eventually found in ~ 80% of z=0 spiral galaxies. This redshift evolution is quantitatively consistent with existing data from the COSMOS survey (Sheth et al.2008), although the detectability of bars is presently limited to z<0.8 because of band-shifting and resolution effects. We predict later bar formation in lower-mass galaxies, also in agreement with existing data (e.g., Sheth et al.2012). We actually find that the characteristic epoch of bar formation is the epoch of massive thin disk formation, corresponding to the transition between an early violent phase at z > 1 and a later secular phase. Bar formation thus traces the emergence of the disk-dominated morphology of today's spirals.