The really tight slow speed u-turns take determination to practice and master. Doing it with everyone watching is the worst, so practice on your own. You must believe this – if others can do it, so can you; it just takes practice. Due to the stress involved (not wanting to drop the bike) I usually get hot and uncomfortable within a few turns. Any type of learning is not exactly fun, but the satisfication afterward makes up for it.
Doing circles are great, but I’d get dizzy quickly so I do fig-8s, except I’d do two full turns before reversing direction. Don’t worry about how small the circle is at first. Pick a diameter that’s comfortable to you, and as you go around the circle in a steady state and get used to it, you can gradually tighten the circle without much effort. Within 15 minutes of practice you’d notice the difference. Eventually you’d trust yourself and the bike enough to totally relax the muscles, allow the handlebar to go into full lock, let the bike does what it needs to do, and that turn will really tighten up. 1 hour of this practice is about as much as I’d want to before I’ve had enough of it (mentally and physically) each time.