Hi Tosin,
It is not feasible to modify the above script(posted by Ravi) for it.

For BP Legacy, there is no separate js for notifications. BP Nouveau does have a separate js file for notifications but it depends on the buddypress-nouveau.js.
So, in case of Legacy, you can not have notifications and disable others and same goes for the Nouveau template pack.

Regards
Brajesh

Hi, You may use the following code in wp-content/plugins/bp-custom.php.
It will break any BP dependencies loading scripts/styles on front end though.

/**
 * Disable 'bp_enqueue_scripts' action by unhooking the function.
 */
add_action( 'plugins_loaded', function () {
	$priority = has_action( 'wp_enqueue_scripts', 'bp_enqueue_scripts' );

	if ( false !== $priority ) {
		remove_action( 'wp_enqueue_scripts', 'bp_enqueue_scripts', $priority );
	}
} );

We are simply making the action ‘bp_enqueue_scripts’ unavailable.

Regards
Brajesh