For base assumptions (Since you haven't mentioned the specs of your solar system), we are going to take our Solar System for a start.
In case you are trying to mass mine water ice from asteroids in the Asteroid Belt, which is located between the orbits of Mars and Jupiter, you would be hard pressed to find water in the Asteroid Belt. It's a straight pain in the a** to find enough water to provide water for a single spaceship.
Based on this paper, there is only about 100-400 billion gallons of water in the asteroid belt. And thats not per asteroid, that's the TOTAL AMOUNT of water in the asteroid belt as a whole
400 billion gallons may seem grand enough. But only till you realize that the total amount of water on Earth is 326 quintillion gallons. The asteroid belt contains about half the amount of water present in Lake Huron. And that means each asteroid would contain a tiny miniscule proportion of water in them. Of course there are exceptions like Ceres, that contain a lot of water. But as I said, on average, it is as hard to scavenge (yes, scavenge) water in the asteroid, as to move a truck by using fireworks.
However, there is a lucky spot in the Solar system, that is rich and juicy (yes "juicy") with water-
Pluto's crib The Kuiper Belt
If your humans have access to the Kuiper Belt, they are GODDAMN LUCKY.
Based on this paper's estimates, if you could gather the entire mass of the water in the Kuiper Belt, you can gather as much as 5 EARTH MASSES worth of water. This would rival GJ 1214b (An ocean world with 8 Earth masses) in terms of water present.
Your humans could send large mining probes (manned/unmanned), to mine out the asteroids/comets in the Kuiper Belt, to get a ton of water from each asteroid/comet. Since each comet (I am going to stop using "asteroid") is rich and juicy with water, your planet could easy get wet and drench to the brim with water quickly.
Happy mining comets!!!