1. Do no try to go straight. Move the handlebars violently left and right when you feel you are falling left or right.
2. Going slow is hard. Go fast. The wheels spinning will behave as stabilizers, making it easier to stay on the bike.
3. Moving your body will make you fall at first if you do not counteract by moving the handlebar. Start by going downhill, without pedaling.
Seems like a lot of people I see on the street never learned how to countersteer and turn or change lanes with alacrity.
I can already guess an answer to this, but would you mind expanding on it anyway? I tend to do this on my bicycle a lot.
However, if I try to introspect...supporting my weight with my arms tends to conflict with the counter-steering part. If I push on the left side, the motorcycle leans that way. But one instinctively pushes on something to hold oneself up. So I think I would say my brain gets subconsciously conflicted over whether to push or pull.
Unfortunately, sport bikes typically have a seating position that makes it very difficult not to put weight on your wrists unless you have good leg and abdominal muscles.
Basically, the faster you go, the easier it is to influence your balance on the bike. If you go fast enough you can get too much influence, which is how speed wobbles happen.
Bicycle wheels do not have enough mass to impact handling through gyroscopic inertia. They do not act as stabilizers.
Motorcycle wheels do, and consequently they require more effort to lean at higher speeds as well as require additional lean when accelerating into a curve.