Hello,
there is more our customers using older version of php. But how wrote mattd, with php 5.3+ it should be repaired.
But we have prepared modification which should be available in newer versions of booking and should work in php 5.2.
Go to administrator/components/com_booking/helpers/html.php and around line 618 should start method getMonthsSelect.
Modify it to this code:
 
    /**
     * Get months select for quick navigator. 
     *
     * @param string $name name of HTML select box
     * @param int $selectedMonth selected month from user request
     * @param int $selectedYear selected year from user request
     * @param int $deep set calendar available deepth 
     * @param string $attribs custom HTML tag params
     * @return string HTML
     */
	function getMonthsSelect($name, $selectedMonth, $selectedYear, $deep, $attribs = '')
    {
    	$arr = array();
 
		$date = JFactory::getDate();
 
		$m = $date->toFormat('%m');
		$y = $date->toFormat('%Y');
 
		for ($i = 0; $i <= $deep; $i ++) {
    		$date = JFactory::getDate("$y-$m-01 + $i month");
			/* @var $date JDate */
			$arr[] = JHTML::_('select.option', ((int) $date->toFormat('%m') . ',' . (int) $date->toFormat('%Y')), ($date->toFormat('%B') . '/' . $date->toFormat('%Y')));
		}
        return JHTML::_('select.genericlist', $arr, $name, $attribs, 'value', 'text', $selectedMonth . ',' . $selectedYear);
    }