Nothing underneath cycle bibs or shorts generally, no. Some people wear underwear but that extra layer of fabric can chafe. On a commute ill wear briefs under the Lycra but that's because it's a shorter ride and I'd prefer not to get my lad out at work, it just feels wrong. Long rides, just shorts.
You don't need much to keep legs warm really, they're doing all the work so keep pretty warm. Blocking wind and having a fleecy layer of Lycra does enough generally, much like a wetsuit on a scuba diver.
On top of bib shorts you wear a jersey like normal. When its cold my top half goes base layer, bib over the top of that, then jersey over bib straps, then jacket if needed.