Can I use the Interactive Brokers Trader Workstation while using TradeBullet?

Yes. Trader Workstation (TWS) must be running before TradeBullet can login to IB. Actually, TradeBullet logs-in to TWS, not IB directly. You can start TWS manually but it is recommended that you let TradeBullet start TWS so all TWS pop-ups windows and reconnections can be handled automatically for you.