One thing to keep in mind is grain orientation. It isn’t the law, but it is a good idea to keep the grain in the same orientation on all pieces of wood. When the grain switches from side grain to end grain, glue loses most of its holding ability. If you live in a high humidity area, this is even more important.
The good news is that it isn’t hard to do. If your vertical spacer is 3/8” wide (for example), you simply need to crosscut a long board into 3/8” strips so that the grain is in the direction that the grain runs around the bowl and then cut those strips into the thickness of the ring. If your vertical spacer is made from multiple pieces, cut all of the pieces this way and glue those strips together before you make the Final Cut to make the final vertical spacer group.
This will make the grain go around the board on all of the wood in a ring. Obviously, when you glue segments and vertical spacers where the grain is running around the board, the glue joints are mostly end-grain to end-grain. But the total strength of segmented bowls comes from gluing rings to rings because this is gluing flat-grain to flat-grain. The glue between segments is simply to keep them together until the ring-to-ring gluing happens.
The first thing that seasoned segmenters look at when viewing segmented bowls is grain direction and it is for good reasons.