What distance are you racing?

I race only short-course (Sprint/Olympic) and I prefer the one piece kit. It provides full coverage - I don't have to worry about the jersey pulling up on the run or bike. Nor do I need a place for nutrition. I have both sleeved and sleeveless suits and I've raced both wetsuit and non-wetsuit in them. I don't usually have to worry about in-race bathroom breaks so that's not an issue. My Desoto FliSuit is great for the before race bathroom breaks (at least for #1), though.

Sorry about not posting distance. I normally just do Xterra races so figure Olympic distance.

A tri suit is more comfortable wet, dries quicker, is less bulky on the swim and especially on the run. In other words, the main difference is the comfort of the chamois and I think that's important. If you're bothered about time in transition, the time taken to put on a jersey is not nothing, especially at sprint or olympic distance.
I've never done a triathlon in cycling gear but I did several duathlons and adventure races that way before starting triathlons. It worked fine, but a trisuit feels better. A one piece tri suit is the most comfortable to race in as far as I'm concerned. A two piece works fine and has the advantage of quick bathroom stops, but that's unlikely to matter for olympic distance so I'd go one piece if I was you.

I wear a tri suit (Kiwami Amphibian Prima) for Xterra races.

Mainly so I don't have to worry about a swim skin.

I have never tried swimming in just a cycling bib. I just assumed that it would be significantly slower than a tri top or trisuit. The shape of a cycling bib seems like it would allow water in the top and significantly increase drag, not to mentioned having more skin exposed. Am I wrong here?

I don't see any disadvantage to wearing a cycling bib and jersey (tight fitting jersey) for the bike, run portion. Comfort is a factor for me, but could be different for you. Normally cycling bibs have a thicker pad, which can be obtrusive during the run.

Depending on the bibs, most cycling chamois will take on a bit of water on the swim, and feel like a wet diaper for the rest of the race... a tri suit offers a bit less padding, but thinner, faster drying and more comfortable to swim and run with. I personally prefer tri kit.. One piece tends to be my preference, although for longer races (once you start thinking 70.3 type distances), a two piece tri kit can be a good idea for the sake of nature breaks (bibshorts would be even worse than a 1 piece try kit, trying to get out of those in a port-a-john when you need to drop the kids off at the pool is not fun).

For some duathlons, where the roads are a bit rougher, and the runs are not too long, I'll sometimes opt for a TT Skinsuit, but otherwise it's tri kit for me...

Thanks for the help. I will look at the tri-kits this year. Got a couple of weeks before the team window closes.

Swimming in bib shorts sounds like a chafing disaster waiting to happen on the bike and run. Biking in a tri kit is no less comfortable IMO than bike shorts, and will make life so much easier during a race. Most Olympic distance races won't have somewhere to change, so if you start in bib shorts you have to do the whole thing in them, and that sounds like an incredibly miserable experience to me. Running in bike shorts isn't fun.

And Nudity in the T zone is a DQ (towel changes are usually counted as nudity)...

The pads inTri shorts/Tri bibs/one piece suits are cut to work with the aero position.

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Since I so Xterra races, how will the fit be when NOT in TT aero position? Riding a mountain bike tends to be a little more upright.

Thanks