A Hohmann transfer is a single ellipse tangent to both orbits — two burns, minimum flight time for a two-impulse transfer. A bi-elliptic transfer instead overshoots far past the target radius on a first ellipse, burns again at that distant apoapsis onto a second ellipse, then burns a third time to circularize down at the target.
At very large radius ratios the Hohmann's first burn has to do almost all the work of escaping the inner orbit's deep gravity well in one shot. Splitting that job — coast out cheaply on a highly elliptical orbit, then adjust far from the planet where speeds are low and burns are cheap, then drop back down — uses less total Δv, even though the path is longer and the flight time is much greater. The crossover between the two strategies sits at a target/start radius ratio of about 11.94, first derived by Sternfeld in 1934; pushing the intermediate apoapsis even farther keeps shaving Δv off the bi-elliptic total, with steeply diminishing returns.
All values are computed live from the vis-viva equation, normalized so the starting orbit's circular speed is 1.