For a Hohmann transfer to Saturn, I get 15.7 km/s for both burns. The transfer time is also a simple formula. I obtain roughly 6 years.
Compare to the lunar ice. It is roughly 2.8 km/s to get to, and the trip time would be a few days, even from Low Earth Orbit.
As suggested by the other answer, you could compare to Earth's surface. If we're using some reference frame far from Earth's surface, then it's nearly 12.8 km/s going up (EDIT: corrected from newbie mistake, LEO gets Oberth). But this gets complicated. The first 9 km/s is constrained by atmospheric physics. Although, leaving the moon also has a similar thrust-to-weight requirement placed on the rockets by gravity drag.
These numbers aren't totally fair to Saturn. If I use the edge of the rings (nearly the "F" ring), I get an orbital velocity of 16.6 km/s. In order to mine these rings, you'll need to follow a hyperbolic trajectory, and then do your final Hohmann burn when you're close to your destination, inside Saturn's gravity well. This will reduce the Delta V you'll need for the final burn. That'll reduce the final burn by a little bit. Breaking up the 15.7 km/s, the initial insertion burn is 10.3 km/s and the heliocentric circularization burn is 5.4 km/s. So we would need to correct this all for the Oberth effect, which is a multiplier of $\sqrt{1 + \frac{2 V_\text{esc}} {\Delta v}} $, sphere of influence assumptions, yada yada. That reduces the previous numbers to (respectively) 5.8 km/s and 1.4 km/s. Boy that was an unpleasant calculation, but the total comes to approximately 7.2 km/s.
Commentary:
It's true that mining the lunar ice would involve challenges that Saturn's rings don't have. But if the destination is close to Earth, those challenges would be more workable than the nuclear, ion, or whatever kind of drives that a Saturn hauler would involve. A similar tradeoff might present itself for other sources closer than Saturn, for instance, Jupiter trojan asteroids.
I won't dispute the quality of Saturn's ice. It is likely more pure than the alternative sources. It might also be in convenient size chunks. Importantly (in its favor) it can be delivered by drives with a low thrust-to-weight ratio. Any value would do for this, although there might be some Delta V penalty due to reduced Oberth effect. Solar electric would be penalized heavily due to the distance from the sun. Nuclear power sources are vastly superior at that distance. 9.5 AU --> squared means 90 times less power per unit area than near Earth.
The real problem is justifying that 6 year time frame. Who is going to wait 12 years for their return on investment? Now I grant you, because of the absence of a gravity drag penalty, it's possible that a ship of monstrous size could deliver huge quantities of ice. Because you're not dealing with any surface-to-orbit transition, your ship could be fragile, and your engine could have a low thrust. Given that, the only thing that scales directly with the payload is the propellant. If we can get something like 30 km/s reaction velocities, then it's believable that making the round trip would work... although only if you can cannibalize water for propellant, and at somewhat poor margins.
So, sure, there is a business case in a very specific scenario where we have a mature market for water in space, someone could reduce costs of procurement by making a ridiculous-looking bloated spaceship that runs the Saturn to Earth orbit route. I'm still not convinced that it would be better than other alternatives beyond the frost line, but most of those have angular clustering. A business might want deliveries more than once every year, and for that, Saturn versus Jupiter trojans (for instance) provide some seasonal diversity. But the advantage is nil except for with extremely large quantities. That raises the question - how could the depreciation possibly compete with lunar ice? If you can run regular ferries from lunar poles to orbit, that seems more economic unless your bloated Saturn ship could be much lower cost (because the lunar scheme has much higher trip frequency). Maybe it could. We can't really say. The biggest variable will be your rate of return. If you demand 6% rate of return, then you're effectively cutting the value of the ice in half over 12 years. This is why it's a hard sell, but that's not really the rocket science part of it.
Addition: Found the example of a "bloated spaceship" that I had in mind. Saw it on Atomic Rockets. Here is the original source. Apparently they had Phobos in mind.
I have some problems with their off-the-bat assumptions. If Phobos has water, why doesn't Eros? I don't know these things. I'm doubtful that anyone else knows the bulk composition or the difficulty of refining the below-the-surface precious water of such inner system bodies. Myself, I would like to picture that "spaceship" with the bladder being 100x its above relatively size. These things will make a hot air balloon look lean.
