Is centripetal acceleration an inertial acceleration?

There is a net force being applied to the ball (by the bowl). You cannot assume that just because the bowl does not move it implies that the bowl is not exerting a force on the ball. Try it with a paper bowl and see whether your ball can still "complete a semi-circle" or not. Not only is the bowl exerting a force on the ball to prevent it from going straight, whatever is supporting/holding the bowl is exerting exactly that same force plus the force needed to negate the gravitational force on the bowl+ball. If it is a flat table, it does so via friction. You can see this if you use a normal bowl but put it on a slippery surface where it can slide freely.