I agree it has limitations. You're method looks more suitable if you are wanting regular large doses.If you're looking to get a large amount of magnesium without drinking a lot of water, you can't use soda water. There is a limited amount of carbon dioxide in soda water, and it is the limit to which magnesium hydroxide will react to produce magnesium bicarbonate. With a carbonator, you can keep on adding carbon dioxide to enable more magnesium bicarbonate to be produced.
If you only want small doses, or if you want to try it out on a small scale before investing in more equipment, the bottle method seems a reasonable option. I've seen recommendations that suggest drinking it quite dilute - more dilute than can be attained by the method I described.