BuddyPress.org

The BP search form is generated from the bp_search_form() function.

Short answer is you can’t modify that function.

But you can add this to your BP member theme:

<form method="get" id="searchform" action="<?php bloginfo('url'); ?>/">

<label class="hidden" for="s"><?php _e('Search for:'); ?></label>

<div><input type="text" value="<?php the_search_query(); ?>" name="s" id="s" />

<input type="submit" id="searchsubmit" value="Search" />

</div>

</form>

Copied and pasted from default Kubrick WP theme.

That should work, but report back and let me know.