Before beginning your tatting, add the number of beads you will need for your project onto the shuttle thread. You may want to add a few extra just to be sure you have enough. Until you're ready to make the HCR, keep the beads far enough down the shuttle thread that you can wind them on the shuttle as well as having more thread wound on the shuttle on top of them. That way they stay out of your way while you work.
Before you pass the working thread around your hand to make a HCR, pull the beads down that you need. Wrap the thread around your hand as usual, making sure that the beads are behind your hand. Leave them there until all the stitches on the HCR are done, then close it. The beads will stay on the single thread portion of the HCR.
You can see an example of this on my Cello star pattern.