Although you have curved your twigs to fit snugly against each other by sanding the ends, the joins between twigs can be very weak. Sand the bark off the upright sections where the joins will meet to make sure the join is wood to wood, rather than wood to bark.
To add even more strength, glue small sections of wood dowel (I used toothpicks) into holes in the ends of your twigs where the joins will be. Use a miniature drill or pin vise to drill short holes suitable for sections of toothpick, and glue the toothpick into the hole as shown in the photo on this page.
When it comes time to assemble the bed section, drill a corresponding hole into the other piece that needs to be joined, and apply a bit of glue to the exposed end of the dowel that will go into it. Insert the dowel on one piece into the hole on the other, and press them together firmly, clamping them if possible. Leave to dry.