Am I correct about what AC/DC BAT BUS does?
You can't easily link the two AC buses together, you'd need to synchronize the phases first. And then a short on one side could cause a complete failure so you'd have to isolate them again. Way to complicated to get that failure tolerant. Instead they just use two independent AC systems. Generally each system exists twice and each one gets a different power source.

In the A320 you have two main AC buses (AC 1 and AC 2) in flight these are powered by engine 1 and 2 respectively. And there is a AC essentials bus, which is either connected to AC bus 1 or if that bus is unavailable it is connected to AC bus 2. The AC essential bus can also get power from the DC essential bus via essential transformer. So you can run the captain PFD and ND and the upper ECAM on battery power (only available above 80kts or sth. or in the air - for emergency only)

Check out the A320 "electrical system descriptions" and "indicating and recording" http://www.smartcockpit.com/plane/AIRBUS/A320.html

At the bottom of the indicating/recording systems you have a bus equipment list telling you exactly which consumer uses which bus. This is true for all other sections as well, so if you are interested in a particular system you can quickly find out where it is powered from. 

According to A320 FCOM, 1.31.75 Indication/Recording Systems, Electrical Supply, Bus Equipment List


  
  AC ESS bus powers the captain PFD and (via AC ESS SHED) the captain ND, the upper ECAM screen, the display management computer (DMC) 1 and
  3 (if selected and AC1 failed), flight warning computer (FWC) 1 and SDAC1. (and many many other things ...)
  AC 2 powers F/O PFD, ND, lower ECAM, DMC 2, FWC 2 and SDAC2 (...)
  AC 1 powers the DMC 3 normally (...)