I've done a good amount of screen printing. So let me get this right, are you trying to screen print your logo onto the bottles? Or are you screen printing onto labels that you will then stick on the bottles? Or am I missing something? If the first, then you have to first choose how many colors you wish to use. Normally, when screen printing onto glass you will use one color as using more than that will cause headaches and is mostly only done by professionals. Also, there's a technique called etching that gives a similar effect by chemically reacting with the glass. In addition, you can use decals that are pre-cut or laser-cut to produce similar effects (will def. cost you a pretty penny). Going back to screen printing directly on glass, what you will use instead of inks are 'enamels'. In a similar fashion to screen printing on fabrics/paper (after you have created your image on your actual screen) you will apply the enamels to create your single-colored image. Then, once the enamel is dry and you are content with the clarity/consistency of your image, you fire the glass bottle/s so the enamel is permanently fixed.
Hope this helps you in some way! Good luck with your image making! BTW, props for perusing such a difficult way of getting a beautiful image!