First I'd like to say that I'm no expert, but I've made my own magnesium supplements for a while now, including mag. bicarb. solution.

Anyway, I don't think you're really making magnesium bicarbonate; I believe the chloride has a greater affinity for magnesium ions and will keep it from reacting the same (or at all). I haven't tested magnesium chloride with carbonated water myself, though.

A good way to tell: is there still carbonation? If you shake your bottle of carbonated water after adding the magnesium, does it still fizz a lot? To test whether or not you're even getting a reaction, add a couple times more of the magnesium chloride and let it sit for a while, then test for fizzing.

If your method is working, however, that doesn't necessarily mean you're ending up with magnesium bicarbonate. I don't know what the chemical reaction would be like for what you're using, but other people giving mag. bicarb. recipe variations a try have ended up with magnesium carbonate (not bicarb) and oxide. I believe the reason the original recipe calls for sodium hydroxide is because it's very efficient and the product is clean (can be entirely mag. bicarb).

Totally not an expert... but I find the easiest and probably cheapest way to do it is still to use the magnesium hydroxide powder, measuring about 80-85% tablespoon per 1 liter of highly carbonated water. The end result is a mostly non-fizzy, kind of milky-tasting water. Sometimes I add a full tablespoon mag. hydroxide and let it do its thing, then pour all the clear solution off the top and throw away any at the bottom (because of the white sediment from un-reacted excess, or whatever else forms and falls out of solution).

Also note that transferring mag. bicarb solution to a glass pitcher may for whatever reason cause it to crystallize against the sides and at the bottom. I don't know why it does this for me... and I wonder if it's staying mag. bicarb! But it performs pretty much the same.

Hope this helps!