diff -u b/core/modules/media/js/commands.es6.js b/core/modules/media/js/commands.es6.js
--- b/core/modules/media/js/commands.es6.js
+++ b/core/modules/media/js/commands.es6.js
@@ -24,7 +24,14 @@
       progress: {
         type: 'throbber'
       }
-    }).execute();
+    }).execute().done((data, textStatus, jqXHR) => {
+      // Warn the user when closing the dialog.
+      $('#drupal-modal').on('dialogbeforeclose', (event, ui) => {
+        if (event.originalEvent) {
+          return confirm(Drupal.t("Closing this modal will cancel the upload process.\n\nAre you sure you want to close?"));
+        }
+      });
+    });
   };
 
   /**
diff -u b/core/modules/media/js/commands.js b/core/modules/media/js/commands.js
--- b/core/modules/media/js/commands.js
+++ b/core/modules/media/js/commands.js
@@ -14,7 +14,13 @@
       progress: {
         type: 'throbber'
       }
-    }).execute();
+    }).execute().done(function (data, textStatus, jqXHR) {
+      $('#drupal-modal').on('dialogbeforeclose', function (event, ui) {
+        if (event.originalEvent) {
+          return confirm(Drupal.t("Closing this modal will cancel the upload process.\n\nAre you sure you want to close?"));
+        }
+      });
+    });
   };
 
   Drupal.AjaxCommands.prototype.addMediaToWidget = function (ajax, response, status) {
diff -u b/core/modules/media/src/Form/MediaBulkUploadForm.php b/core/modules/media/src/Form/MediaBulkUploadForm.php
--- b/core/modules/media/src/Form/MediaBulkUploadForm.php
+++ b/core/modules/media/src/Form/MediaBulkUploadForm.php
@@ -104,6 +104,15 @@
       return $form;
     }
 
+    // If only one type accepts the current file, skip the type selection.
+    if ($form_state->get('step') === 'select_media') {
+      $file = $form_state->get('current_file');
+      $valid_types = $this->filterTypesThatAcceptFile($file, $types);
+      if (count($valid_types) === 1) {
+        self::mediaTypeSelectSubmit($form, $form_state, reset($valid_types));
+      }
+    }
+
     $form['progress'] = $this->getFormProgress($form_state);
     // Determine what step of the form we're on.
     switch ($form_state->get('step')) {
@@ -261,10 +270,16 @@
   protected function buildMediaForm(array $form, FormStateInterface $form_state) {
     /** @var \Drupal\Core\Entity\EntityFormInterface $media_form */
     $media_form = $form_state->get('media_form');
+    if (!empty($form_state->get('files'))) {
+      $save_value = $this->t('Save and continue');
+    }
+    else {
+      $save_value = $this->t('Save and finish');
+    }
     $form['subform'] = $media_form->buildForm([], $form_state);
     $form['subform']['actions']['submit'] = [
       '#type' => 'submit',
-      '#value' => $this->t('Save and continue'),
+      '#value' => $save_value,
       '#submit' => [[static::class, 'mediaFormSubmit']],
       '#ajax' => [
         'callback' => [static::class, 'mediaFormSubmitCallback'],
@@ -334,16 +349,27 @@
     $form_object = $form_state->getFormObject();
     $media_form = $form_object->createMediaForm($file, $type);
     $storage = $form_state->getStorage();
-    // Remove storage values set by the previous media form - this prevents
-    // previously submitted values from appearing in new forms.
-    $storage = array_diff_key($storage, array_flip([
-      'entity_default_langcode',
-      'langcode',
-      'form_display',
-      'entity_form_initialized',
-      'field_storage',
+    // Remove all unknown values from form state, to ensure a clean media form.
+    $storage = array_intersect_key($storage, array_flip([
+      'total_files',
+      'current_file',
+      'files',
+      'step',
+      'media_type',
+      'media_items',
     ]));
     $form_state->setStorage($storage);
+    $input = $form_state->getUserInput();
+    $input = array_intersect_key($input, array_flip([
+      'form_build_id',
+      'form_token',
+      'form_id',
+      'ajax_page_state',
+      '_drupal_ajax',
+      '_triggering_element_name',
+      '_triggering_element_value',
+    ]));
+    $form_state->setUserInput($input);
     $form_state->set('media_form', $media_form);
 
     $form_state->setRebuild();
@@ -363,6 +389,7 @@
   public function createMediaForm(FileInterface $file, MediaTypeInterface $type) {
     // Move the temporary file to the correct destination.
     $location = $this->getUploadLocationForType($type);
+    file_prepare_directory($location, FILE_CREATE_DIRECTORY);
     file_move($file, $location);
     $media_form = $this->entityTypeManager->getFormObject('media', 'add');
     /** @var \Drupal\media\MediaInterface $media */