"I would assume it would be a better idea to drink the water 45-60 minutes after you injest the hydrogen peroxide to make sure it's not too diluted or wasted and passed out as urine. "
You might have made an error in what you typed and what your thoughts were, but I suggest you do some research regarding injesting 35% Hydrogen peroxide. No way should you injest 35% H202 without it being diluted with water.
Also there is plenty of information out there that suggest that consuming any H202 may have a downside. I know there are some on this board that don't believe it, but you should at least be aware.