Why do doctors say to drink lots of water when you are constipated, doesn't it just make you feel more bloated?

It's the truth. Many cases of constipation are due to inadequate water intake. Water should not make you bloated as it is absorbed into the tissues or passes through into the colon very quickly. More water in the colon creates softer stools that move more quickly through the colon.
Maybe. The colon(large intestine) recycles water from the gut. The less water in ones diet the harder the stool. Increase water in the diet and the colon absorbs the excess and has to work less harder. One does not have to drink water to excess. The rule is an ounce of water for each pound of body weight.