Hi Timothy,
You could use the Profile Search widget to add a search form in a sidebar or widget area, or the [bps_form]
shortcode to add a form in a post or page.
If you wish to add a form in a different place, you have to add a line of code in the relevant template:
echo do_shortcode( '[bps_form id=1234]' );
Replace 1234 with the actual ID of your form.