We sold these in the shop I worked at. These were the suspenders everyone used: Vintage Cycling Rainbow Stripes Suspenders World Champion Bike Bicycle Shorts | eBay

If it isn't immediately obvious that bib shorts work better for you, they clearly you don't need them. The point is to prevent the fabric from bunching up in or just above the genital region.

These days I'm usually inclined to wear hiking shorts and a t-shirt most of the time. OT but I've noticed that this often rubs people the wrong way if they are all outfitted in the proper kit and a fancy carbon bike.