How do you randomly zero a bit in an integer?

Updated with newer answer and better test

Let's say I have the number 382 which is 101111110.

How could I randomly turn a bit which is not 0 to 0?

The why;

Since people ask me why, I simply need to do this, removing a bit from an integer.

based on the answer here is the result(working one)
I ran this

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.Diagnostics;

namespace ConsoleApplication1
{
    class Program
    {
        static Random random;
        static void Main(string[] args)
        {
            Stopwatch sw;
            int[] test = new int[10] { 382, 256, 1, 257, 999, 555, 412, 341, 682, 951 };

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    Perturb(test[j]);
                sw.Stop();
                Console.WriteLine("Perturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> Perturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    FastPerturb(test[j]);
                sw.Stop();
                Console.WriteLine("FastPerturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> FastPerturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNe