Thank you for your answer.
I made a function that worked, but I do not know why it does not work since the last update (i’m not developer) :
function displayBilingualLinkerURL(){
ob_start();
the_bilingual_link();
$urlString = ob_get_clean();
$pregStr = "#<a href='(.*)'>(.*)</a>#";
preg_match($pregStr, $urlString, $bUrl);
echo $bUrl[1];
}