They are stored in pokeballs to save space. That's why items you find on the ground in the games are in pokeballs.
Pointing something unusual out IS NOT COMEDY!!!!!!
The bike folds, it's in the description of the bike
Pshh, they're collapsible.
Your a child roaming a land full of magical beasts that you control through a small ball and this is what you question?
Not sure if there is a bike that can fit in a bag but I've definitely seen a fishing rod fit in a backpack.