Solarization is supposed to use a clear plastic to exploit the greenhouse effect. I don't know if black will work very well. Did you have disease? I don't know why this would be necessary for container media unless it was for seed starting. Of course that would only be a couple gallons.

Black plastic also works and does have the advantage of light-starving sprouting weeds. But, as Nil mentioned, unless you are trying to kill off grass/weeds in a bed or have had an issue with disease, is there some particular reason you feel the need to sterilize the dirt?

When reading about reusing soil I've come across some articles that mention cleaning the soil from the past season. Since the soil has been outside from previous season exposed I figured it sounded like a good idea. If I don't need to then that's cool too, saves me a step :)

The solarizing soil studies have suggested 3-4 weeks in July California sun.

I'm not sure zone5b can get your bags hot enough, but what do I know? I've never measured the temperature deep inside.

I'm sure it's a matter of personal choice, but I would never bother sterilizing potting soil for any reason other than seed starting (and I don't do much of that at all). Unless you are using a high quality, structured soil mix like the 5-1-1 or gritty mix, potting soil should be replaced every season. It just doesn't hold up long enough to be used indefinitely and by the end of a growing season, has collapsed to the point where it is no longer efficiently aerated or well draining. Diseased stuff - regardless of mix - just gets tossed.