Actually the intuitive human reactions on a bike are often the exact opposite of what you need to do to balance the bike. F.ex. if you look at kids learning to bike their intuitive reaction to the bike falling to one side is to lean to the opposite side, but that has the exact opposite effect of what they want to achieve. When you lean to one side you exert force force on the bike the other side and the bike will fall quicker. What you need to do is to use the handlebars to turn a little bit to the same side the bike is falling to re-balance it. Ehm, at least I think so? The more I think about it the more uncertain I become.

Veritasium does an experiment on this exact topic: https://www.youtube.com/watch?v=9cNmUNHSBac