BART trains have these spots for bikes, with adjustable straps to hold bikes upright. But with a strap or two secured the bike still rolls back and forth as the train moves, which lets it knock into things.

The way to prevent rolling is to hold down a brake lever. You can do that with a large velcro strap, or your hand. But if you don't have a strap, and you want to sit down, you can wrap your helmet straps the handle, and connect the buckle. If needed you can twist the straps to make them shorter. You don't have to press the lever all the way down, just enough to stop the wheel from rolling.