How to bypass mechanical doorbell

I have installed a Ring Video Doorbell Pro and it works OK. But, the existing mechanical doorbell will not work with the Ring like it is supposed to. (It is rings constantly or periodically depending upon which way I connect the wires.) What is the correct way to bypass the mechanical doorbell? Is it safe to go directly from the transformer to the Ring Video Doorbell Pro without the mechanical doorbell in between? I have attached a diagram of the way it is wired now. Thanks.