"zone" connectios are for two-channel use, not 5.1.
As for zones, these are generally "line level" (red/white RCA jacks) outputs which require additional power amps to drive speakers. Some 7.1 receivers allow you to reconfigure them use two of their internal power amps for this if you are running a 5.1 system for "zone 1".
I've never seen a receiver that allows the use of two 5.1 systems.
Plus, all receives I've seen that allow an additional zone only allow this for analog sources so 5.1 would not work, anyway.
But, if your receiver offers "A" and "B" speaker outputs, you can run a stereo pair to the bar. These will share most likely an existing amplifier with whatever speakers are running the "A" channel. I think there are some exceptions that allow extra internal amplifiers to be used for these though.
Personally, since to you want to run both stereo AND 5.1 in the bar, I'd consider a separate receiver and source for this.