A little information from a local source (scroll down some for the worms)
From Missouri I think
From the folks who seem to know the most on composting in general
Using non-native worms or importing worms seems to be an issue for glacial north america. I don't think it's an issue for non-glacial places like LA but I wonder sometimes if we really need any more imports.
I'm about half a degree latitude north and 2 degrees longitude west from you I figure. Riverside I believe gets hotter in the summer and the higher altitude ensures it gets colder in the winter. My thoughts for a worm bin were to keep it in the garage out of the sun and the wind and the extremes. I'm betting that would work for you too.
If we stray from the strict confines of a worm bin, you could just push 4 pallets together secured with bailing wire to form a box open top and bottom. Let the bottom rest on the bare ground or on pavers sitting on the bare ground (keeps the tree roots and the burrowing critters out). Fill the bottom with with browns (dry woody stuff like leaves and wood chips - bark chips will take far too long to break down so avoid them unless you like the challenge). Add the standard compost mix of greens and browns in a slow as you go method with what you have on hand. Keep moist. Cover the top from sun, wind and rain. when you build it, the worms will come. Big time when the rainy season comes and the worms are looking for an unsaturated refuse from the very saturated ground. As long as you keep that sucker from drying out, it will be full of worms in 6 months or so. You will find that as you add, the bin contents will reduce in volume so it could be almost forever filled with your regular refills. You will have lots of worms until stuff finishes.
The worms you end up with will be native or at least naturalized and not imported. They will leave their cocoons so as you spread your compost you will spread fun happy worms.
With the worm population of a 3 x 3 x 3 pallet bin, you will have enough worms to start any happy worm bin you like when you're ready. Pallets free, worms free, worm food free. Very low labor. What's not to like?
Keep moist. Keep out of sun and wind to help moisture levels and temperatures from getting too hot.
An interesting little thing on raising worms - fast.
I don't have a worm bin. I'm only thinking about it. I have pallet bins on pavers as described above. We get desert winds and the marine layer but overall we're on the dry side. Build it and they will come.