As elegant as you want to make it (no tux!).
The restaurant is fun with a group .. more intimate with just a couple..... HOW you dress in Vegas is not so much how comfortable YOU feel with yourself. I mean jeans and sandels would probably be in poor taste unless you have lots of diamonds around the neck! Bling bling!
I wore jacket and silk shirt (round collar not polo) and was very comfortable ... my business dinner companion wore jacket and Polo dress shirt no tie.
Staff attitudes are most forgiving.. A LOT depends on if you order high priced wines and such .. a large table of 'foreign' travelers with numerous children got GREAT service since the wines were very very flowing to the adults! More tip, more service!!!
Um, at the Bellagio, are you getting a regular room or suite??? Some up-scale rooms (and of course HiRollers) will get the VIP service team that can be most helpful .. I would not go back with them again. I think my 'level of service' (fantastic) was based not on my clothes but that VIP Concierge made the reservation!
You GOTTTA see 'O'!!!!