At least the size of a nickel! 8)

I'd use a pot big enough it doesn't need watering twice a day. Perhaps quart sized or so. That should make it a little less sensitive to the watering schedule. I assume you will put it outside in the spring?

I'd put the ziplock bag in the fridge to slow the other bulbs down. You don't want them getting moldy either. Putting them in pot now would (IMO) help prevent mold. I've overwintered (dormant) Lilies in pots in the garage. Problem is they take off very early in the year since the garage isn't cold enough.