Photoshop Bitmap / Halftones with transparent background

Halftones are automatically created when screenprinting... you don't need to make them in Ps. 
Talk to the printer and they'll show you how this works.

It looks like your design is two colors, black and white, plus transparency. You could select all non-transparent areas, and save that in a new grayscale doc. This will be for your "white" ink. Select the inked areas, and save that as a new grrayscale doc. This will be for your "black" ink. Now you can convert both of those to bitmap, and overprint the "black" over the "white".

Here, I've made the two as Solid Color layers, to illustrate how they stack (over a solid gray layer):

"white":

"black":

Composite:

If you're looking to add a halftone effect without converting your file to a bitmap (so that you can maintain the transparency), you could either apply the Halftone Pattern filter (Filter > Filter Gallery and inside the filter gallery go to Sketch > Halftone Pattern) or install the free Comic Kit script and apply it.