BuddyPress.org

I’m not aware of a plugin that can do exactly that? Perhaps some of the guys on here know of one?

To do it manually, you could hook a function to init and work from there. For example:

function my_function() {

    if ( ! is_user_logged_in() && bp_is_current_component( 'messages' ) ) {
        // Current user is not logged in so don't let them see stuff. In this case, private messages 
        wp_redirect( home_url() );
        exit;
    }
        
    $flag = false;
    // Get current user info.
    $user = wp_get_current_user();

    if ( ! in_array( 'student', $user->roles ) ) {
        // The current member is not a student.
        $flag = true;
    }

    if ( $flag && bp_is_current_component( 'messages' )  ) {
        The currently logged-in member is not a student and is trying to view private messaging. Let's redirect them away.
        wp_redirect( home_url() );
        exit;
    }
}
add_action( 'init', 'my_function' );

From that, you should be able to see how you can achieve what you’re trying to do without the need of a plugin.

Refs:

Template Tag Reference

https://codex.wordpress.org/Function_Reference/wp_redirect