Phenomena in a molten bridge between electrical contacts at the stage preceding vacuum arc ignition and their influence on the arc duration are investigated using a mathematical model and experimental data. Two models of a bridge are considered and compared. The first model is based on the representation of a bridge as a melting filament between contact surfaces, while the second one describes bridging as extension of a liquid metal drop between contacts. The initial conditions for the temperature fields of electrical contacts at bridging start are formulated taking into account heat transfer in solid contacts before bridging. Evolution of a bridge during contact opening, its length, radius, time and coordinates of bridge rupture at boiling temperature are evaluated depending on electrical current, opening velocity and parameters of contact materials. The above mentioned mathematical model enables estimatation of the density of metal vapors in contact gap just after bridge explosion, which is responsible for vacuum arc ignition and maintenance at the initial stage of arc burning. It was found that bridge duration and anode arc duration is interrelated. There exists a critical contact gap, which becomes too large to support the power capacity required for the maintenance of extending zones of anode melting and evaporation. If the length of a bridge exceeds this critical gap, then the anode arc phase could be not appearing at all. On the contrary, if the bridge length is negligible or if the bridge does not appear at all, then duration of anode arc phase is maximal.