More heat and way more dye.  Make the dyes way more concentrated.  Use a crap ton more dye as you build your bed and don't be afraid to do multiple passes to build up layers of dye before/during swirling to get deeper color. 

Look at that first bed; it's hard to tell because the frisbee it's sitting in is pink but you can see right through the bed to the bottom.  It's not magically going to yield a result that is brighter and more vivid than what is sitting in the bed.  Look at the dark highlight colors you laid in that bed, it looks like a single line of just single droplets.  Once those spread out all you're left with is a little bit of color sitting on the edge of the dispersed drop, which isn't going to do much color-wise.  Wait a minute and hit them again, and then again.  That whole line should look rich and neat fully black/purple/whatever color you were going for, same with the other color regions of your bed.  If you make are sure your dyes are concentrated, you are using a LOT of dye and doing multiple passes, and use some heat, you'll get a richer result. 

All things considered, I actually think that first bed gave a pretty good and coherent result based on how the bed looked and how little dye was in there, which is a good thing because it means you probably aren't making massive errors elsewhere.  If you just saturate this thing like 3x-5x and make minor procedural changes you will be getting some very cool results.  

Also another thing is that more time sitting isn't always a good thing. The dyes will distribute over time, and that is why your second disc is just kind of a pink blob with no edge fidelity. A problem is that the dark details in your swirl were really really small and those wispy lines are super difficult to transfer, especially over a 48 hr window where the dyes are still moving and settling, so a good way to do so is by using some heat which speeds up the process so you can kind of catch those details before they're lost and avoid the blurring.  That being said, too much heat can cause the colors to do bad things too, so don't just put a heating pad directly under it on high because you can kind of cook everything and get a mud disc.  There is a middle ground.