Is there a particular time of year a birtch tree sheds it's bark?

You have a Paper Birch Tree!

Yes you are eye witnessing a normal of the tree's cycle of growth. Each late winter or spring when it grows, like a snake sheds it's old layer of bark while growing a new layer. So this is normal. This can happen anytime the tree grows however.

Two times are common, in summer...exactly the few weeks is impossible to state as it depends on where you live...as the tree puts on another wood later. Then again late winter as the tree starts brining in more water from the roots to begin flowering and leaf out. But you are right, there is some shed throughout the year. Still look around for unusual holes which could be a borer....look around the base at the soil line.