for starters, unless you're keeping the bin in a totally dark environment, paint it or wrap it with something, light is not good for worms - in addition 4.5 gal isn't big enough for much action, it'll be difficult to maintain ideal conditions .... you certainly won't need a 'collection bin' to feed that small a worm bin, even with a larger population, you won't be able to add much food waste [the primary thing to use, in addition to paper/cardboard bedding] without it heating up from bacterial action

OTOH, bacteria is what you want - worms can survive on carbon alone, like leaves and paper, but the point of a worm bin is usually to take care of kitchen waste so it doesn't attract critters to the outdoor compost bin ... if you want castings, but usually bin compoat your kitchen waste, then feed the worm bin on freshly finished hot compost, they love it and will turn it into castings, as well as increasing their own population so you don't need to waste more money buying worms

a short answer is you can add anything to a worm bin that you'd add to a compost bin, but you have to consider the overall management - temp and moisture are the most important things, along with the need for all feedstock to become microbially active before it'll interest the worms, and the fact that they can only eat so much

Bill