You might want to try sublingual vitamin B12.

Although I rarely watch daytime TV, one day I caught a few minutes of Dr Oz, who was asking the audience to stand, close their eyes and count to 10 or 15, then open them up. He asked if anyone felt dizzy. He said those who did might have a B12 deficiency, and noted that B12 is not absorbed in the gut, but under the tongue instead. I take 5000 units daily. Does it help? I don't stumble much.

But I still drink on the bike only while coasting at moderate speeds.