The normal rule is that nudity in the changing area will result in disqualification, though it does happen occassionally.
I use an all-in-one tri-suit with a light padding in the butt for the cycling. It dries out quickly enough on the bike, though like everything else in triathlon it takes a little getting used to. I would recommend practising your swim-run transition at some point to get used to changing when wet (things like "should I take the time to put on socks?" get sorted out when you actually try it out).
If you're not worried about padding, then probably best to cycle in your swimming trunks and just pop on a top after the swim.