A BE-30 pilot reported that a high performance single engine aircraft taxied on to BOI Runway 28L without clearance. The crew queried the aircraft's runway position where upon ATC issue a go-around and cleared the incurring aircraft for takeoff.

Narrative

Conducting a visual approach to Boise Gowan Field (KBOI) at the end of an IFR leg. We were cleared to land on 28L following a regional jet on final for 28R with a caution for wake turbulence. We acknowledged and proceeded. I was Captain and my partner was at the controls. On short final Aircraft Y; that was holding short; taxied onto the runway at the departure end. Being focused on reviewing the landing checklist; I don't recall the Tower issuing a clearance to the Aircraft Y to enter the runway. My partner asked if Tower had cleared the aircraft onto the runway and transmitted the question on tower frequency. Tower hesitated; then told us to execute a left 360. Being fully configured and close to the ground; I gave the command to go-around; add power and accelerate straight ahead; then I selected flaps approach and we began a climb. We extended upwind in order to clear the new tower under construction; then Tower cleared us to turn left downwind. As we flew downwind; Tower cleared Aircraft Y for takeoff. We were then cleared to land; turned final and executed a normal landing. Everything normal after that; nothing said by Tower or Ground to us.Because of the sequence of events and the fact that our approach had been a long straight-in; we believe Tower had forgotten us and had cleared Aircraft Y to enter the runway; then was momentarily surprised by us. The obvious thing is that had we not taken action; we may have hit the aircraft on the runway. Aircraft Y did not clear the approach area before entering the runway and tower did not give either of us any commands until we spoke up. While it wasn't razor close; it was much closer than ever should have occurred.A classic runway incursion. Vigilance is the only way to avoid these events. Complacency is the enemy.