For those that want to use 2 quickbar sets in order to have their General Skills in different quickslots for 2 different spec builds there is, to my knowledge only one workaround that will accomplish this, at least until Turbine fixes this bug.
The key to getting the memory to hold is clearing your character of all specs and specializations prior to switching Quickbar Sets and loading a new Spec Build.
The term Hotbars as used below means a set of quickbars, the ones you can swap (Shield/Sword/Horse)
From my Guide;
However if I like to have different setups of General Skills according to my spec a couple of issue arise.
If I try to do it on all on one Hotbar I have to manually move my General Skills each time I switch specs and that usually means some if not all Trait Skills are going to auto populate all over the place.
To get around this;
Manually place General Skills on both Hotbars 1 and 2.
1) Arrange General Skills on Hotbar 1 about where you'll want them for Spec 1. It doesn't need to be perfect yet..
2) Arrange General Skills on Hotbar 2 about where you'll want them for Spec 2.
3) Go back to Hotbar 1 and load Spec 1. Now you can move your General Skills and Trait Skills around to where you'll want them.
4) Staying on Hotbar 1, load Spec 2. I'd move the new Trait Skills into a Cluster somewhere they'll be easy to locate.
Please note that as of Beta 6 at this point things stop working as expected! There appears to be some kind of bug where the memory function gets messed up. At least I hope it's a bug because the workaround as I detail below requires the purchase of another Spec Tab. Store purchase to implement expected basic functionality is unacceptable. I will update this as functionality is either confirmed, changed, or fixed.
EDIT: UPDATE
Sapience has posted that the memory is indeed not WAI and a fix is on the way, although likely not until after Patch 12.1
5) Purchase a 3rd Spec Tab on your Trait Tree Panel. Do not choose a Specialization or put any Points into this Tab, you want it blank.
6) Click this Tab, Tab 3 so that you "despec" or get back to a point where you have no Specialization chosen and no Trait Skills on your Hotbars.
7) Switch to Hotbar 2 and load Spec 2.
8) Arrange General Skills and Trait Skills as you want them for Spec 2.
9) Load Tab 3 to despec.
10) Switch to Hotbar 1
11) Load Spec 1
All of your Trait Skills should auto populate correctly for that Spec and all your General Skills will be in place for that Spec.
As long as you load Tab 3 and despec yourself before switching Specs or Hotbars everything will auto populate correctly for you. If you forget to despec your first change will work fine, but when you change again that Spec layout will be lost.
If you are running 2 Hybrid Specs and want your General Skills in different Quickslots the issues get really bad. Since Trait Skills always attempt to auto populate the Quickslot they last occupied there is no way I've found to have shared Trait Skills auto populate different Quickslots depending on Spec.
Pretty much you will always have to repopulate manually any shared Trait Skills between two Specs. The best you can do is try placing your general skills in a fashion that requires the least amount of manual population. This is another area that need attention badly.