There was a scrappy stop-start opening to this game as both sides looked to grab hold of the game.
It was the hosts who made the breakthrough on just before the quarter-hour mark when Bosma was able to find the net with a well-placed header to open the scoring.
As Truro looked to fashion a response, some neat play from Niall Thompson saw him make progress towards goal before firing well over.
With 26 minutes on the clock, Eastbourne managed to double their advantage when a teasing ball in from the right found Romain who managed to guide the ball beyond the reach of Martin Rice.
On a 3G surface it gave City a mountain to climb and Rice had to be alert on a couple of occasions to prevent the home side from further extending their lead as the first half came to a close.
Early in the second half and Rice again did well to push out a curling free-kick from the hosts that was on target.
As an effort from distance dipped just over for The White Tigers, try as we might we were unable to breach the home defence who stood firm.
Our cause wasn’t helped with five minutes to go when Arran Pugh was dismissed for a second yellow card having halted Romain’s progress.
We refused to let our heads drop and some neat link-up play between Les Afful and Tyler Harvey saw the latter just wide before in stoppage time, an inviting high ball pumped into the danger zone found the head of Rocky Neal who went close.
It was huff-and-puff but ultimately brought no reward as we went down by two goals to nil.
TRURO CITY: Rice, Knowles (Smith), Richards, Booth, Bentley, Pugh, Brett, Harvey, Yetton (Neal), Thompson (Afful), Allen. Subs not used: Cooke, Byrne.
Booking: Allen. Red card: Pugh.
ATTENDANCE: 539.