Bow ties are generally considered formal evening wear, not business attire, much like tuxedos.
I'd also actually put the 2 piece suit with tie over a 3 piece suit (with or without tie) in terms of formality/business-attire-ness: 3 piece suits are also not traditional business wear, while 2 piece suit+tie is the IBM/'50s iconic business look, and what you'd see most CEOs/etc. wearing.
I'd also actually put the 2 piece suit with tie over a 3 piece suit (with or without tie) in terms of formality/business-attire-ness: 3 piece suits are also not traditional business wear, while 2 piece suit+tie is the IBM/'50s iconic business look, and what you'd see most CEOs/etc. wearing.