Index: src/wp-includes/js/media-views.js
===================================================================
--- src/wp-includes/js/media-views.js	(revision 29578)
+++ src/wp-includes/js/media-views.js	(working copy)
@@ -4956,9 +4956,12 @@
 				return;
 			}
 
-			// Add 'selected' class to model, set aria-checked to true and make the checkbox tabable.
-			this.$el.addClass( 'selected' ).attr( 'aria-checked', true )
-				.find( '.check' ).attr( 'tabindex', '0' );
+			// Add 'selected' class to model, set aria-checked to true.
+			this.$el.addClass( 'selected' ).attr( 'aria-checked', true );
+			//  Make the checkbox tabable, except in media grid (bulk select mode).
+			if ( 'library' !== this.controller._state ) {
+				this.$el.find( '.check' ).attr( 'tabindex', '0' );
+			}
 		},
 		/**
 		 * @param {Backbone.Model} model