One of the cycling disciplines I enjoy most is time-trialling. The courses are usually "out and back" along a straightish piece of road. This means they almost always will involve a u-turn.

Initially I wasn't confident, but we have a kilometre of flattish straight road from our gate, so one of my regular rides is to ride this back and forth along this.

So to do a 10km ride, I have to do 9 turns... a 20 km ride (verrry boring, but I do that sometimes) involves 19 turns.

This is what has made me good and relatively quick - but definately confident doing tight u-turns.

Practice, practice, practice... thats all I can say.
It is about getting to know how you and your bike feel and realising its ok... it takes time, but you get there.

Do it slowly in a car park, get a cone or some obstacle you can bike around, and over time - hours, days or weeks - turn closer and tighter to the cone.