This decorative wire by Oasis comes in two different weights and many different colors. It is also available in flat wire for a different look.
I just start at the top and carefully rotate the bouquet, winding the wire tightly around itself.
Carefully unwind the coiled wire as you move down the bottom of the handle. I like leaving part of the stems to show to continue with the "illusion" of a true hand tied bouquet.
Finish at the bottom by cutting with wire cutters and twisting the cut end up inbetween the flower stems. The cut end should be firmly embedded into the floral clay so it can't damage hands or dress fabric.
You can see by a photo underneath how the wire is tucked neatly up into the bulging floral clay.
Don't wind the wire so tightly that you lose the "flared" look that you worked so hard to obtain.