I usually use a 5 inch pot (planting 5 tulip bulbs), watering twice a week.
Yes, I also have roots sticking out of the bottom of the pot, but I don't think its the main reason of failure. Provided that you don't let the soil dry out completely, I usually have a 80% of flowering rate
I think the trick is to make sure that your tulips come into flowers in about 30 days (in Hong Kong), otherwise the bulbs have a very high chance of rotting.
I think I may give them much water, when the soil or the bottom was dry, I would give water to them.
I remembered that during Chinese New Year, there was a long holidays, around 9 days, there was no watering during that holidays at my office. However, surprise, they grew faster than before.
After taking David's advise. I do not water the tulip bulbs too much in this few days, I try to keep track of the growing status by marking their height daily. And I discovered that my tulip bulbs still grow few mm per day, and the bulbs remain healthy.