In its role providing shield bursts, the Bifrost competes with the Stork, which has more tank but less speed. This makes the Stork preferable if it can reach the required speed.
When it comes to skirmish bursts, the Bifrost competes with the Magus (and to lesser extent with the Draugur). If you have shield logistics support you normally choose the Bifrost, if armor logi the Magus. In fleets without logi, the Bifrost is often preferred over the Magus (and the Stork) because of its higher speed.
In Norse mythology, Bifröst was the bridge connecting Asgard, the place of the gods, to Midgard, our Earth.