We had a mountainbike in arma 2 and ever since i got arma 3 i missed it.
It was not very useful, but fun.

I would love to have a nice bike in arma 3.
Either a citybike, that is good on the road and ok on dirt roads,
or a mountainbike with offroad capabilities,
or a road bike, that is fast on the road, but has problems on dirt roads,
or all three ;-)

The citybike should have lights (front and back), the other two maybe not.
You should get fatigued when driving fast (similar to sprinting).
You should also get fatigued when driving uphill with an inappropriate bike.

If you chose to implement the "Advanced Driving Model" i suggested (http://feedback.arma3.com/view.php?id=21844), the bicycle could even have sequential gear.
The citybike could have 3 gears and the others 6.
The gears could also effect fatigue:
If you drive to slow on a high gear (this applies also if you get slowed down by an incline or bad terrain for your bike).
That way lower gears can help you drive uphill.

Maybe the bicycles and a few new cars could be include in a future DLC and the "Advanced Driving Model" in a free update, that goes with it (like the helicopter DLC).