Since you are adding quite a bit of water in your Blast, definitely include that in your total water consumption.
To increase water intake, drink fluids (water) throughout the day when you are not Blasting as well. No need to intersperse water between sips.
If you have a bottle filled with water with you at all times it will remind you to sip on it throughout the day. Shoot for at least half of your body weight (pounds) in water (ounces).