<a href="https://vborg.vbsupport.ru/showthread.php?t=228112" target="_blank">This article</a> explains how you can make your own "blank" vbulletin page, say membercard.php or something.
In the template it instructs you to make don't put the header, navbar, or footer... just put the HTML you need for the member card- should give you a good start on this.