What features should I look for when buying bib tights?
This is a somewhat subjective topic as everyone has their own personal preferences.

But for me (a skinny 30 something riding in Scotland where winter is typically -5 to +5°C):

Fabric: Generally a thick 'roubaix' style brushed lycra for warmth.  Windproof fabrics tend to be less flexible/comfortable and I would only use them in extreme cold weather.

Padded: No. You can wear your existing shorts under non padded tights.  If they have their own pad, they need to be washed every use, without a pad the tights can be re-worn after some rides.

Straps: Personal preference.  Some prefer the higher waistline and extra material for warmth.  Personally I prefer easier natural breaks as riding in very cold conditions makes them a more regular occurrence.

Water resistance: I find DWR treatment an amazingly good feature on tights, with splashes from puddles just bouncing off, keeping you much drier and warmer.  Softshell type materials (which are also usually coated) will be even more water resistant, but have their own drawbacks (covered above).