Because all that energy you put into speeding the bike up helps keep it going straight, and that force fights against little wobbles side to side.
When you are stationary, there’s no forward force to fight the side-to-side wobbles, and so instead you have to move your body weight around to counter them.
So the same small tipping forces that make you wobble are always there. But the momentum of the bike does all the work for you fighting against them when the bike is in motion.
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