At least where I am, DUI is specific to motorized vehicle operation - if you’re on a bicycle or a horse or whatnot, your ABV doesn’t matter, as long as your drunkenness doesn’t interfere with safely using the roads.
Having an open beer on a bicycle is no different from having an open beer on foot - you can get ticketed for either, but it’s under the liquor control act, not the highway traffic act.
