After Gammie commented on my failure with kumihimo and beads, I just had to try again.
Originally, I was trying to run a thin thread alongside the thicker thread and that didn't work so well. Following Gammie's suggestion, I strung my beads onto Fireline and didn't add any thicker threads.
The picture shows two examples. The one on the left is all size 10/0 seed beads - 8 different colours. I started it using one bead at a time and then to speed it up, I started adding 3 beads at a time and I like it better.
The gold and pearl example uses two threads with pearls and 6 threads of size 10/0 seed beads. I moved 5 seed beads every time and it turned out quite well I thought.
Neither example is ready for prime time. I keep forgetting where I am and messing up the pattern, but I now know I can make it work so one of these days I'll set it up properly and make a bracelet.