Array, HashMap, Strings - how to send it via Bundle?

This is bad encapsulation, poor object oriented thinking.

It sounds like you need a Song abstraction so you can return a List of Song instances:

List<Song> songList = new ArrayList<Song>();

I would avoid Java serialization; serialize them as JSON using Jackson.

ArrayLists and HashMaps are serializable objects. So just use Bundle#putSerializable(bundleKey, serializable).

If you want a more OOP approach, you can encapsulate the data to be sent into an object (say of type SongData) that implements Parcelable. See this post for an example. Also see the reference documentation for Parcelable:

public class MyParcelable implements Parcelable {
  private int mData;

  public int describeContents() {
      return 0;
  }

  public void writeToParcel(Parcel out, int flags) {
      out.writeInt(mData);
  }

  public static final Parcelable.Creator<MyParcelable> CREATOR
         = new Parcelable.Creator<MyParcelable>() {
      public MyParcelable createFromParcel(Parcel in) {
          return new MyParcelable(in);
      }

      public MyParcelable[] newArray(int size) {
          return new MyParcelable[size];
      }
  };

  private MyParcelable(Parcel in) {
     mData = in.readInt();
  }
}

In the sender class

bundle.putSerializable("something", songsListData);

and in the receiver class

ArrayList<HashMap<String, String>> songsListData = (ArrayList<HashMap<String, String>>)bundle.getSerializable("something");
;

Use something like the following in the sender

ArrayList<HashMap<String, String>> songsListData = new ArrayList<HashMap<String, String>>();
intent.putExtra("song_list", songsListData);

and than in the receiver class

ArrayList<String> myList = (ArrayList<HashMap<String, String>>) getIntent().getSerializableExtra("song_list");  

ArrayList<HashMap<String, String>> songsListData = new ArrayList<HashMap<String, String>>();
Gson gson = new Gson();
String str_json = gson.toJson(songsListData);
Bundle bundle=new Bundle();
bundle.putString("data",str_json);

Use Gson for converting arraylist data into string

Gson gson = new Gson();
Type type = new TypeToken<ArrayList<HashMap<String, String>>>() {}.getType();
ArrayList<HashMap<String, String>> arrayList = gson.fromJson(data, type);

For retrieving data in reciever class