Today I practiced on this stitch some more. The stitches are much better now.
Tip- pull the needle towards yourself after piercing the fabric, then make a twist, hold this twist, with your left thumb, then make the chain stitch. I found , this way the stitch tension is more controllable. The sampler till now-

27.bonnet stitch -sampler1

The details-
5. In the first row, two rows of bonnet stitch are worked facing each other. The second row, the up and down version of bonnet stitch.

27.bonst-5

6. Individual bonnet stitches are worked with upright cross stitches in the first row, butterfly chain stitch in the second row.

27.bonst-6

7. Bonnet stitch is worked over straight stitches in the first row, detached chain stitches are worked in between bonnet stitch in the second row.

27.bonst-7

8. Bonnet stitch with herringbone in the first row, and with half chevron stitch in the second row.

27.bonst-8

9. Fly stitches are worked over bonnet stitches in the first row, bonnet stitch is worked over a line of buttonhole stitch variation in the second row.

27.bonst-9

Combining bonnet stitch with some other stitches is the next goal.