'The bath will announce when it is almost ready', is a simple straight forward method of explaining what will happen. As newer baths will sometimes have a warning or announcement, it might seem that you would need to explain in more detail, however, this is quite unnecessary. All that is required is explaining that there will be an announcement or warning.
「お風呂が沸きそうになると知らせてくれます」を伝えるためには、以下のようなフレーズが適しています。 It lets us know when the bath is almost ready. 「お風呂がもうすぐ沸くと知らせてくれます」
また少し詳しく言うなら、 Our bath has a feature that notifies us when the water is almost ready. 「うちのお風呂には、水がもうすぐ沸くと通知する機能があります」 というようにも表現できます。