Private transfer companies with luggage storage, Heathrow to Windsor

Hi,
We are in the final planning stage of our trip to Bath coming up in several weeks. I wonder if you know a private transfer service to Windsor that will also store a couple bags. We have anytime tickets to the castle and plan to catch a train near by to go onward to Bath via London. Is there another way to do this without heading back to Heathrow for the bags? I did read many threads but did not find an answer other than staying in Windsor or London first night which is not an option for us.