Можно использовать библиотеку NAudio, создать класс Mp3FileReader на основе MemoryStream. На C# код будет выглядеть как-то так:

using System;
using System.Collections.Generic;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using NAudio.Wave;

namespace WpfApp1
{
    public partial class MainWindow : Window
    {       
        public MainWindow()
        {
            InitializeComponent();  
        }    

        System.IO.MemoryStream ms;
        Mp3FileReader reader;

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            ms = new System.IO.MemoryStream(Properties.Resources.Mp3Name);
            reader = new Mp3FileReader(ms); 
            
            WaveOut waveOut = new WaveOut(); 
            waveOut.Init(reader);
            waveOut.Play();
            waveOut.PlaybackStopped += WaveOut_PlaybackStopped;            
        }

        private void WaveOut_PlaybackStopped(object sender, StoppedEventArgs e)
        {            
	    //воспроизведение завершено
            (sender as WaveOut).Dispose();
            reader.Dispose();
            ms.Dispose();
        }
    }
}