Excellent question. What kind of containers? Clay, glazed, unglazed, plastic, wood? What is your zone?

We have plastic containers, I live in Canada, zone 5.

Growing bulbs in containers is really quite simple. Unless prechilled and wanting to force into bloom earlier than normal, spring flowering bulbs get planted at the same time as they would in the ground. And keeping them cold and dark is good.....just do not allow the pots to freeze. They also need no water during the winter months but the potting soil should be just moist to the touch. If the soil appears too dry (it shouldn't), just dump a few ice cubes on the pot. Watering them is what would cause any rotting.

When it becomes closer to bloom time, you can move the containers outside so the foliage can grow with some bright light and the plants can set their flower buds.

So should I plant the fall bulbs in pots then now? I can keep them inside for the winter.

You can plant them now. And they can stay outside until the weather gets really cold, although I would store them out of the direct weather (like where the rain doesn't reach them). Once the temps start dropping and freezing weather is predicted, then bring them into store for winter but it must be someplace that stays cold - no more than 45F but above freezing. And light during that storage period is not an issue - it can be quite dark as the bulbs are doing all their work below ground and do not need any sunlight until the foliage starts to appear.