335okc has a point - how many miles are on your suspension? Dampers lose their effectiveness over time. Uncontrolled motion is what makes a car's ride feel, well uncontrolled/unnatural. The stock dampers are underpowered as-is to provide the illusion of a 'supple' ride hence you get bounced around (the damper design philosophy of even big name suspension companies is to do as little compression damping as possible when in fact they should be doing the opposite).
Side note: thanks for the descriptive, concise, and properly punctuated explanation of your issue; lately we've experienced a tragic shortage of intelligence amongst thread starters.
2011 BMW 335i E92 - Le Mans Blue, 6MT, M Sport. JRZ RS Pro, Quaife LSD, BMW Perf Exhaust