I've ridden many times over the Inlet Beach/Carrillion Beach 98 bridge. No official bike lanes, but wide enough shoulders so it's not a problem. I usually stay in Seagrove, and will ride over to Laguna to grab doughnuts at Thomas's; and also ride 98/30A down to Destin.
Your route - I don't recall bike lanes on the 331 bridge, nor lanes that continue all the way up to route 20. And it's been a while since I've driven 20 east towards PC, but some sections of 20 are awfully busy.
Last year I decided to ride a couple Saturday rides with the Emerald Coast Cycling Club. Had to drive to the ride starts, but the roads were very low traffic off the beach, and even had some mild rollers. They do have some mid-week rides as well.