I don't stop drinking until the second dose of Epsom Salts . Usually I try to super hydrate until 2 pm by drinking as much as I can without feeling ill. I drink filtered water, apple juice and Master Cleanse lemonade (good for the kidneys) until 2. I drink water and a little juice for energy until the first Epsom salt, then water only until the second drink. I try to stop drinking after that so the stomach is empty when the oil hits it.
It can be hard to find the right balance. The laxative action of Epsom Salt works by pulling water into the colon. It is very dehydrating. On the other hand, the old adage about oil and water not mixing is proven true when the olive oil hits the stomach. You do not want water in you just before taking the oil. You have a good chance of throwing it all up.
Be cautious, but experiment and find out how long you can drink before flushing. Two hours between your last water and the oil/juice should work for most people.