I suggest you take a look at some of Pat Parelli's stuff. Try NATURAL
HORSE-MAN-SHIP. (John Lyons probably has the same advice.) Anyway, Pat
recommends riding with a rope fixed to the right side of the bit, looped
around the neck to make the reins, and attached to the left side of the
bit with about 12 feet left over. Put a couple of loops in the 12 feet
and stuff it into your belt or waistband. This will give you a safe hold
of the horse if you part company, and, when properly adjusted for the
purpose, can be used to tie up the horse if necessary.
Jo