Humans aren't going to last that long, we are in the end-days man, this tired world will be gone in 50 years max. It'll just take one splicing of Ebola or Aids with the Common Cold virus and we're all dead. Get your kicks while you can everyone.
However, IF we last that long;

Rubber will be a thing of the past and wheels (if they still exist) will grip the road with thousands of tiny hairs like fly legs, so the only limit to traction will be how strong the actual road surface is.

Wheels will be able to deform instantly to ride over any obstacle. You could drive at a kerb at 100mph and not feel a bump.

Bikes will have internal gyros, so they can stand up by themselves.

The power source will be tiny, so no petrol tanks. I'm picking the power generator will be a Hawking-Schwartzchild Kernel, with Quantum-buffered plasma over-run conduits to dump excess event-horizon energy.

Bike will weigh maybe 20 kilos or less? There's no need for an engine, instead the power feeds directly into the wheels like an inductive drive, so immediately the bike is lightened by a hundred kilos. The frame can be made of extremely light materials, no need for this carbon-fibre primitiveness, let's go straight to hyperfiber.

Inertial dampeners will stick you to the bike, but they can be turned on or off to capture the feeling of riding in the ancient 20th century.

In the unlikely event that you fall off, safety clothing will be a thing of the past, replaced by a gravity-force-projector beam on the bike that will beam out and grab you, reduce your fall speed, turn you the right way up, and put you gently on your feet, even if the bike is on its side 50m away, which is of course impossible because of the internal gyros and sticky wheels.

Wind and rain will be deflected by an electrostatic field, invisible except for a slight tingling.

Internal computers and an integrated highway system will mean that the bike can ride itself at almost supersonic speeds, the only limit being imposed so people living near highways don't suffer from sonic booms.
That's all I thought of right now. Oh, and Sprotsbike riders will turn all the safety gadgets off and crash often.
There will still be lots of antique motorcycles powered by infernal combustion engines, but as oil will have run out, the antique enthusiasts will have to run them on home-brewed ethanol.
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