Intent intent = new Intent(this, MostrarDatos.class);
  intent.putExtra("usuario", edsuario.getText().toString());
  startActivity(intent);`

try{
        Bundle bundle = new Bundle();
        bundle = getIntent().getExtras();
        txt1.setText(bundle.getString("usuario"));

    }catch(Exception e){
        Toast.makeText(getApplicationContext(), "¡A ocurrido un error!", Toast.LENGTH_SHORT).show();
    }