You could do it, similar to Thermahippy's advice, only just use 1 supply battery. I would take 2 resistors, maybe 3.3 kohms each, in series, with the middle point call it: " AC ground".
So, casually approached, you've then got 12 VDC supply, as + and -, and you've created an AC ground, that could be attached to any metal case, and any sheild grounds.
For a better ground point, (DC) I would consider using a pair of 9 V batteries, that being less power, if (and when) something on the bench (accidently) contacts places it shouldn't. So you would have one of the 9V as a (-9V rail), )with it's positive connected to ground, and the other 9V battery as a (+9V rail), having it's (-) connected to ground. Then that's a good time to check your work; before hooking up any IC.
With that full plus and minus rail set, and valid ground, you won't need to create the 2 resistors divider, or the cap. Suggested put a capacitor from ground to each rail (observing correct + and minus on any polarized capacitor.)
So that's 2 batteries and 2 capacitors, like maybe 100 uF each should be adequate. Many designs feature putting a second capacitor, tiny mica type, for absorbing the really tiny bit high frequency noise spikes, as the little cap.s are faster acting, than a power capacitor, like 100 uF.
Keep in mind; Standard 9V batteries don't have rediculously high capacity, for long running times.