How can you prevent lettuce from becoming bitter?
I think the key here is that you've been buying oversized lettuces. Bitterness of lettuce plants is not something under your control. When the lettuce matures (on the plant), it eventually starts flowering (called "bolting") as a way to perpetuate its genes. Once this sets in, the leaves turn bitter due to the production of certain chemicals, and acts as a defense mechanism against insects. 

The process of bolting is irreversible and if it has commenced in the plant, it will continue on in the cut lettuce head (perhaps at a diminished rate). Big lettuce heads are invariably more mature than the smaller ones, which is why you experience a higher occurrence of them turning bitter. You could try the other suggestions here, but I cannot say for/against any of them as I haven't heard of any of them being used to control bitterness.

My advice would be to buy small to medium sized lettuces. Young leaves are tender and less likely to turn bitter. One might be tempted to buy the biggest lettuce on the shelf so as to "maximize" the leaves/dollar, but in the end, you have to decide whether the bitterness is really worth it.