I use my basket top to scatter the pieces onto the mat. It works because my basket lid has a graduated lip which allows the pieces to easily flow over the edge.
There are several ways of casting your bones. I have a large set with some large pieces, so I cast by sprinkling them onto the cloth from the lid of my basket. My basket top has a graduated curve on the lip, so it works well for this purpose. Lids that have a vertical lip would make this much more difficult. If my basket lid were not suitable, I would probably purchase a taller basket and sprinkle them from it like sprinkling food from a canister.
If your set will fit into your hands this is obviously the easiest way to cast them. You must practice getting a good distribution of the bones. Dropping them from too high up will result in them spreading out too widely with few groups of bones to interpret. Dropping them from too close to the cloth can result in a big clump that will be difficult to read. When this happens, you can still read them in layers picking the top pieces off to see what is underneath as you interpret them. Or you could just read the top layer, though this may make for a short reading. In my mind, it is better to practice your throwing so that you know the right height to throw from. This height may change over time as you add and remove pieces.
When I first started, I experimented with different ways of casting. I tried having the client cast the bones. This did not work well as most clients had no idea of how to go about it, and even with my advice often got a bad outcome with the bones either in a clump or throwing them all over the place. Next, I tried throwing all the bones myself except for the bone representing the client. I would have the client throw that piece into the thrown bones, using its position as my starting point. This worked well. But as I started doing more distance readings, I was unable to do it, so I just throw all the bones now. You might want to try this method if most of your readings are done in person.
When I get a poor distribution (it happens), I do not rethrow. It is what it is. I just get through it as best I can. I don’t believe in rethrowing the bones. That is like redoing a tarot reading because you did not like the answer (I must confess that I have been there, done that).
If you can hold your set in one hand dropping it onto the mat is probably the simplest way to cast. You just have to find the right height to drop from to get get consistent result in how they spread out.
Sprinkling the bones from a container usually works well no matter how many pieces you have.
Swirling the bones on the mat is a method I have been seeing more recently. I think practice is required to get a good distribution, but it works well, especially with larger sets.