There hasn't been much about this written yet. So just two directions:
1) The easiest way to submit a bizform with partial postback (via AJAX) is to enable Use update panel
in the web part properties / AJAX.
2) If you need to trigger additional scripts on the partial postback (e.g. refresh some dynamically generated elements of a form), then generally in OnContentLoad
event of the web part placed inside UpdatePanel, the code should be run after partial postback.
You could try to use our ScriptHelper class to register the script... there are two overloads of RegisterStartupScript, one uses the Page and one the Control, maybe that would be helpful -
public static void RegisterStartupScript(Control control, Type type, string key, string script)
If the aim is to show the bizform in an effect window (like lightbox, thickbox, fancybox etc.), the key thing is to keep the form code inside the form tag that we render in the output HTML.
Optionally please try to describe your aim in more details so we could find a possible solution. Thanks.