switch count($params) {
  case 1: mysqli_stmt_bind_param($st, 's', &$params[0]); break;
  case 2: mysqli_stmt_bind_param($st, 'ss', &$params[0], &$params[1]); break;
  case 3: mysqli_stmt_bind_param($st, 'sss', &$params[0], &$params[1], &$params[2]); break;
  ...
}

$sql = "insert into TMP(C1,C2) values (?,?);";
$col = ['C1','C2'];
$val = [[1,2]];
$tmp = 123;

$dbh = mysqli_connect('localhost', 'usr', 'pwd', 'db');
mysqli_set_charset($dbh, 'utf8');
mysqli_query($dbh,'delete from TMP');
$st = mysqli_stmt_init($dbh);
$rc = mysqli_stmt_prepare($st, $sql);
$param = []; $param[0] = str_repeat('s', count($col)); foreach ($col as $v) $param[] = &$tmp; debug_zval_dump($param);
call_user_func_array(array($st, 'bind_param'), $param);
$n = count($val);
foreach ($val as $row) {
        for ($i = 0; $i < $n; $i++) $param[$i+1] = &$row[$i]; debug_zval_dump($param);
        $rc = mysqli_stmt_execute($st);
        print "* #$i: new id " . mysqli_stmt_insert_id($st) . "\n";
}
mysqli_stmt_close($st);
$res = mysqli_query($dbh,'select * from TMP');
while ($row = $res->fetch_assoc()) print_r($row);
mysqli_close($dbh);

array(3) refcount(2){
  [0]=>
  string(2) "ss" refcount(1)
  [1]=>
  &long(123) refcount(3)
  [2]=>
  &long(123) refcount(3)
}
array(3) refcount(2){
  [0]=>
  string(2) "ss" refcount(1)
  [1]=>
  &long(1) refcount(2)
  [2]=>
  &long(123) refcount(4)
}
* #1: new id 39
Array
(
    [ID] => 39
    [C1] => 123
    [C2] => 123
)

$st = mysqli_stmt_init($dbh);
$rc = mysqli_stmt_prepare($st, $sql);
$param = []; $param[0] = str_repeat('s', count($col)); foreach ($col as $v) $param[] = &$tmp; debug_zval_dump($param);
call_user_func_array(array($st, 'bind_param'), $param);
$n = count($col);
$c = 0;
foreach ($val as &$row) {
        for ($i = 0; $i < $n; $i++) $param[$i+1] = &$row[$i]; debug_zval_dump($param);
        call_user_func_array(array($st, 'bind_param'), $param);
        $rc = mysqli_stmt_execute($st);
        $c++; print "* #$c: new id " . mysqli_stmt_insert_id($st) . "\n";
}
mysqli_stmt_close($st);
$res = mysqli_query($dbh,'select * from TMP');
while ($row = $res->fetch_assoc()) print_r($row);

$stmt = $mysqli->prepare($query);

$stmt->bind_param("sss", $val1, $val2, $val3);

$val1 = 'Stuttgart';
$val2 = 'DEU';
$val3 = 'Baden-Wuerttemberg';

/* выполняем запрос */
$stmt->execute();

$val1 = 'Bordeaux';
$val2 = 'FRA';
$val3 = 'Aquitaine';

/* выполняем запрос */
$stmt->execute();