Don't give up on that just yet. I built mine last summer using #6 and a few bees do get through it, but not all that many.
An update on my #6 stainless steel mesh - it's working a treat with not one bee through it yet!
Thanks for the encouraging words David, seems that in theory #6 doesn't work, but in practice it works great, for the 2 of us anyway
A note to add here is that the supplier I got my #6 mesh from has 3 different #6 meshes, the difference being in the wire thickness, therefore the aperture size. The 3 different aperture sizes are 3.3mm 3.0mm and 2.7mm and the one I am using is the largest of them at 3.3mm aperture.