To implement a custom taxonomy task using hooks with Bulk Task Editor register the task:

add_action( 'rewbe_taxonomy_actions', function($actions,$taxonomy){

     if( $taxonomy == 'your-custom-taxonomy' ){

          $actions[] = array(

               'label'  => 'Name of your task',
               'id'     => 'bulk_task_name',
               'fields' => array(
                    array(
                         'name'    => 'var_1',
                         'type'    => 'select',
                         'options' => array(
                              'value_1' => 'Option 1',
                              'value_2' => 'Option 2',
                              'value_3' => 'Option 3',
                         ),                    
                    ),
                    array(
                         'name' => 'var_2',
                         'type' => 'text',
                    ),
               ),
          );
     }
     
     return $actions;
     
},10,2);

Add the callback function of your task:

add_action('rewbe_do_term_{bulk_task_name}',function($term,$args){
     
     if( !empty($args['var_1']) && !empty($args['var_2']) ){
          
          $var_1 = sanitize_title($args['var_1']);

          $var_2 = sanitize_text_field($args['var_2']);
          
          // your logic here
     }
     
     return $term;
     
},10,2);