What Mesh & What Ink ??

the mesh would depend on the design, I would say a 156 mesh would be safe. but you will need to use a gaphic ink, these are a bit fumey, and dry quickly so you will need to move fast, epecially if your design is multi colored.

Paper / Cardboard water base inks
230-305

156 is a bit low, especially for thin paper like paper bags. If you dump too much ink it can bleed and the paper can buckle. Most waterbased paper printing ink won't be bad in terms of fumes (though some are... unpleasant smelling... like gym bag unpleasant), though they do dry in the screen if you don't keep it moving.

I would try this ink:
Naz-Dar 5500 Series Flat Poster Screen Ink - BLICK art materials

I've also messed around with this ink, and it worked pretty well. I was using a 110 mesh and the ink printed heavy, so I would definitely suggest at least a 230.
Speedball Water-Soluble Poster Ink - BLICK art materials