I've been riding shorts with clip-on suspenders for decades. (The mentor of New England racing in my day, John Allis did the same though I suspect he road higher end shorts with the buttons for non-clip-on suspenders.) Back then I wore cotton fishnet tees under my jerseys. I had to keep the straps off my nipples so I ran them through a rubber band to center them (and keep the clips outboard for better abdominal breathing though I doubt that made any difference. I now just move the clips in.
I wonder if bib straps sometimes have the same effect. (I've owned one pair of bibs. The bib version of my favorite shorts. Yeah, a touch more comfortable at their best, but once things stretched out a little, not as good and snug as suspendered regular shorts, more expensive and a lot more hassel in the restroom.)
And a thought I just had. Instead of nipple coverings, how 'bout wearing a silk tee? Very, very comfortable and the same material I wear under my cycling and boot socks for the same reason. (REI has them at decent prices.)
Ben