Wooden beads covered with splints of straw are common straw work decorations. They are simple in concept but a little difficult to do because you need to hold on to the splint while wrapping it around the bead advancing a little at a time around the bead. The hole in the bead is used to draw a straw thread thru so the beads can hang. (example below in pink).

The best way to learn is with a fairly good sized bead in the video below I used a 3/4″ round saucer bead. After the video I have another way to cover smaller beads but they have to have a fairly large hole.
Modified method for covering smaller beads
I found it very difficult to do so I came up with a modified method in which I sew thru an enlarged hole in the bead the first time around and then between the existing wraps for the second time save one or two of the last times around the bead. In the first photo the pink shapes were made the same way as the beads below and have a long straw thread so they can hang with the rest of the straw flowers among the bow. Here is how I’ve done it.
Tools

Some straw, a straw splitter, some straw threads, an awl and some Becon’s Fabri-tac glue.
Method
First you need to soak your straw split it or cut it into 2-3mm splints (the purple come from ironed flat straw so it was cut with a ruler). Then remove the pith with the back of a pair of scissors. This will soften the straw enough that you will be able to work with it without it fraying or breaking.


You should see some fibers on your scissors left behind after the process.
Your straw should curl a bit after the process.


Add a drop of glue to the pith side of the straw.
Stick the glued end into the bead and hold it in place with the awl until the glue dries. I will not call the end with the straw to top of the bead.


Loop your straw around and thru the bottom or the bead and out the top of the hole.
Pull it snug and angle the straw around a bit so that when you repeat the last step this wrap will be about 1 straw width away from the first in the middle of the bead.


It will look like this.
Continue until you have about 8 or 10. You need to have an even number.


If the hole starts to get small you need to stick the awl into the hole and wiggle it around. You can also stick it in the other side and wiggle too.
When you are near the end of the straw splint clip it even with the hole and add some glue and hold that down with the awl.


Splice in a new straw splint the same way you started.
Wrap this splint around the bead until it is almost covered. Each round should be between the existing wraps. On the last wrap do not go down into the whole but wrap around the outside of the bead. This will be the bottom of the bead.


Use a large eyed needle to draw the last of the splint thru the center and out the bottom but make sure that you push the straw that is covering the bottom of the hole aside so you do not sew thru it.
It will look like this. Clip the tail away.


Make a knot in your straw thread. This is what the bead should look like from the top.
Thread the opposite end of the straw thread into a large eyed needle.


Use the needle to sew up thru the bottom, right thru the middle of the splint that covers the hole and out the top.
You should be able to see the knot at the bottom of the bead.


The yellow one is a little different the splints came from a straw tube so it needed to be split (when damp) with a splitter as seen here. The yellow one does not have a straw thread as a stem like the purple so it needs to be finished off another way.
I picked the two that were the closest to the same size.


Then I took the pith off the non-shiny side with the back of a pair of scissors.
You can see the straw splints curl a bit and an amount of pith is left on the blade.


This starts like the purple one above.
It continues thru the first splint as did the purple one.


I got all the way to 10 wraps in the first layer then three times around on the second layer until I ran out of straws
I glued the end of the first and the beginning of the second in place to finish the wraps.


On the last two times around I did not go into the hole. I used the tail end of the splint to make a knot by slipping the end under one of two wraps and pulling it thru the loop. I the purple bead this would be the top of the bead.
This is how the bead looks from the bottom.


I used it as the center of the star flower with the bottom side up and the tail trimmed away. You can see how I made the star flower here.