To enjoy a bi-elliptic savings, destination needs to be greater than destination orbit by a factor of 11.94 or greater.
Going from LEO to the moon certainly qualifies: 384,400/6678 = ~58.
I'll pull a bi-elliptic path out of the hat, don't know if it's optimal:
300 km altitude circular orbit to a 900,000 km altitude apogee: 3.16 km/s
Apogee burn at 900,000 km to raise perihelion to 384,400 km: .43 km/s
Circularize burn at 384400 perihelion: .18 km/s.
So a total of about 3.8 km/s. It's noteworthy that Farquhar's more direct route reaches EML2 for around 3.4 km/s
If you time your burn from LEO to land near a certain region of earth's Hill Sphere, the sun's tidal influence can raise your perihelion to 443,000 km (the neighborhood of EML2). From there the ship can do a ballistic slide into EML2. I describe such a path in EML2 blog post. This can take as little as 3.1 km/s.
So for LEO to EML2 a .7 km/s savings can be enjoyed over bi-elliptic and a .3 km/s savings over the Farquhar route.
Saturn's orbit is less than 11.94 A.U., so no bi-elliptic savings.
But there is no ITN route from earth to Saturn or even from earth to Mars or Venus.
"What?" you may ask. "How come the earth-moon-spaceship 3-body system confers savings while the sun-rocky planet-spaceship 3-body doesn't" The difference is in the 3 body mass parameter.
All kinds of interesting trajectories emanate from the Pluto/Charon L1 and L2. Ditto Earth/Moon L1 and L2 as well as gas giant/big moons L1 and L2
But the sun/small rocky planets mass parameters are in the millionths to hundred millionths. I don't believe there are any interesting WSBs leading from the sun earth L2 to Mars or any other planet. At least none that take less then centuries to arrive at the destination.