Pull it back far enough that it will not get pushed back onto the bark again later. Does not matter what it is, burying stems of woody plants can produce problems.

Coarse bark is less effective for weed suppression than fine bark at an equal depth. OTOH, fine ground Hemlock bark will sometimes shed water when packed over time unless a texture is put on it. I have even poked holes in it with a pitch fork to allow water to seep into the ground. That's was when I was doing yard makeovers and new construction. Appropriate groundcovers should be planted and occasionally top dressed with compost to do the work of just a straight mulch. I prefer woodchips in my own garden. The price is right, and it looks more 'organic' than sterile looking bark. In a few cases I put down wood chips for a customer and then top dressed with bark for a more refined look. A bit more labor intensive, but the final product turns out looking nice.

I'd say that, like wood chips coarser bark particles would be more effective at suppressing weeds than fine ones. The finer the texture, the more like potting medium or soil a mulch is and the more suitable it is for germination of seedlings. Aged, medium to fine bark under trees used for perching by berry-eating birds may sprout little thickets of holly, Oregon grape, cotoneaster, firethorn etc. if not kept weeded.