As bonsai birch--including paper birch--aren't easy. If you want that attractive white flaky bark, you will have to grow the cutting out in the ground for a decade or so. In a pot, it is slower to appear.
If you want the white bark, starting with a tree that already has it is the way to go. The new growth on a cutting will not have it.
In bonsai cultivation, like most pioneer species, it will sucker from the base constantly, drop limbs for no reason--limbs that may have take you five years to develop.
It can make striking bonsai, but you have to put up with alot...