be sure to include a method in your form:
<form name="..." method="post" action="...">
also, be consistent: you've gone for $SESSION['...'], so do that with $POST too, don't use "'s.
also, have you defined your user_id session elsewhere?
I always find it's a good idea to echo out your SQL statement and then copy it into PHP my admin (if it looks good on screen - sometimes you find that a variable's not going in properly) and run it there. the error functions are much better there.
also, you can redirect using header() (in php) providing you've not outputted to browser at all:
header("Location: /bio_updated.php");