The way you are doing is it the normal way it is done. It is possible to do it more directly, but you would have to run an ntrip server on your phone and it would also have to have a public IP address.
I think it is best to have a middleman, such as rtk2go. Also you could rent a server and set up your own NTRIP server if you wanted (or run it on a computer from your home or work). It depends why you want to do it this way (privacy, least cost, full control, etc.).