Abundant Asteroid Belts

Shortly after getting more serious about mining, I have ran into a problem of asteroids being depleted very fast. I have chosen a system close to Jita for mining to save on the travel time, but as you can imagine, I was not the only one who likes being in close proximity to the trade hub. Although there are 7 asteroid belts in the system, there's no shortage of miners grabbing whatever ore they can get their hands on (not to mention a fair share of can-flippers roaming around, making jet-can mining impossible). So "the asteroid has been depleted" has become quite a familiar tune. Aside from the initial pride in the whole "I have just mined out the entire asteroid belt by myself!" feeling, the lack of ore has become quite an annoyance. But there are several ways to get a whole load of asteroids all to yourself.

Typically, whenever you accept a mission for an NPC corp, you will have to warp to a deadspace spot somewhere in the system, and there's a high likelihood of you encountering asteroids there. It may be something very common like Veldspar or Scordite, but it'll be all for you to mine nonetheless.

The beauty of this is that unless people will be scanning the system for the locations of players, nobody will know of your secret mining spot. That means that you can safely mine, storing your ore in a jetcan. Of course, nobody is ever 100% safe anywhere in the New Eden, but it is an acceptable risk in my opinion.

To take advantage of the "mission" asteroids, you have to keep the mission open for as long as you want to mine the ore, and that might cut into your bonus reward for fast mission completion. This shouldn't be a problem for missions that give 3 to 5 hours to collect bonus reward. You are very likely to finish the mission and mine every single asteroid out there. But please keep in mind that jetcans disappear after about 1.5 hours. To avoid losing all of your ore, either haul it all to the station and come back to mine more, or refresh the jetcan simply by creating a new one and transferring everything from the old jetcan into the new one.

Aside from taking on the missions, another way to find untapped asteroids is to scan the system for anomalies. From time to time, you will be able to find asteroids in the NPC pirate hideouts or drone bases. However, in this case, anybody else that's after collecting bounties placed on NPC pirates will be able to stumble in on your location. So it is not as safe for jetcan mining.

A completely filled jetcan mined at a (former) drone base

In my personal experience, I have once found a drone base in a hollow asteroid that was surrounded by lots of Veldspar asteroids. One pirate found me eventually and flipped my jetcan, but not before I was able to fill up 2 whole jetcans (2 x 27000 m3) and haul them back to the station. As I said, you're never 100% safe from can-flippers (so take proper precautions with secure containers if you can), but you can certainly mine alot of ore without competition.