Index: src/wp-admin/js/inline-edit-post.js
===================================================================
--- src/wp-admin/js/inline-edit-post.js	(revision 40330)
+++ src/wp-admin/js/inline-edit-post.js	(working copy)
@@ -115,6 +115,15 @@
 		// enable autocomplete for tags
 		if ( 'post' === type ) {
 			$( 'tr.inline-editor textarea[data-wp-taxonomy]' ).each( function ( i, element ) {
+				/*
+				 * While Quick Edit clones the form each time, Bulk Edit always re-uses
+				 * the same form. Let's check if an autocomplete instance already exists.
+				 */
+				if ( $( element ).autocomplete( 'instance' ) ) {
+					// jQuery equivalent of `continue` within an `each()` loop.
+					return;
+				}
+
 				$( element ).wpTagsSuggest();
 			} );
 		}
Index: src/wp-admin/js/tags-suggest.js
===================================================================
--- src/wp-admin/js/tags-suggest.js	(revision 40330)
+++ src/wp-admin/js/tags-suggest.js	(working copy)
@@ -120,7 +120,9 @@
 			},
 			minLength: 2,
 			position: {
-				my: 'left top+2'
+				my: 'left top+2',
+				at: 'left bottom',
+				collision: 'none'
 			},
 			messages: {
 				noResults: window.uiAutocompleteL10n.noResults,