There are two basic ways that the holes in most purchased, gemstone beads have been drilled. If you look at your hand reamer bit you will notice that it is graduated as are the drill bits used by manufacturers. A bead is either drilled from one side to the other, so the hole is bigger on one end that it is on the other; or it is drilled from both sides, which may not line up, so although the bead looks like it has a good sized hole all the way through, inside the hole is smaller and may not be aligned straight across the bead!
Using a hand reamer on softer materials like pearls, malachite, fluorite, etc will work better if you ream under water and use a continuous in and out motion. The diamond reamer used is actually grinding the material away, which collects on the reamer and needs to be flushed, both off of the reamer and out of the bead. The water also acts as a cooling agent and a lubricant for both the bit and the material.
On harder materials (agates, quartz, etc) you may find that using a press for a dremel or a flex shaft will work. Again, always work with the bead underwater at slow speeds, in and out, and use quality diamond bits. Be sure to wear safety glasses to avoid accidents if the bead should shatter.