I was wondering if it's okay to layer the bulbs? For example I'm thinking of planting my oriental lilies on the bottom-most layer, and since I can't have a lot of pots on my balcony, I thought maybe I could plant a different kind of bulb in the middle layer and then something that just grabs onto the top layer of the soil? Beginner container gardener here, so I need help!

There should be no reason why you can't do it with the lilies, although you might want be aware about how the lilies multiply. Thus dividing might be in order at some point (and with a mixed pot, if the bulbs are close to being similar in size, you might end up mixing them up). I know I have 2 pots of asiatics with tons of babies and I really really really need to get in there and divide them (too lazy...lol).