There was not that big of a skill jump when reaching Barbarian Bowl from Bone Pitt. Although I was facing against tougher opponents, I relatively won most of my matches with ease. With a wider variety of cards, however, it was harder for me to counter the new cards that came with reaching Barbarian Bowl. Especially the rocket, which took almost all my troops except for Giant and Valkyrie, although leaving it at such low health.
Here's my deck: