This is the hallmark of the hunter-style braid, the most common, and in my book, most elegant braid. Tie the yarn under the bubble in a double knot and snip off the excess yarn. Not to worry, snip out the yarn and start over. Tidy braids will come over time and practice. And even if your braids never resemble Graf George's at the Olympics, don't worry.
Judges value even a so-so braiding job.
They will appreciate your efforts anyway. The same braiding technique applies to the forelock. You may have to have a friend hold your horse's head because it's hard to braid a forelock if your horse is swinging his head around. French braid the top of the forelock. Incorporate the yarn when you begin the simple braid section.