Aaron Wilbraham gave the home side an early lead with a tap-in after Bolton keeper Paul Rachubka denied Joe Bryan.
Lee Tomlin scored from a Nathan Baker long ball, before Peter Odemwingie made it 3-0 from distance and Scott Wagstaff tapped in Jonathan Kodjia's pass for 4.
Kodjia then headed home Adam Matthews' delivery and Bryan's right-foot strike finished the scoring for City.
With 8 games remaining, the Robins remain 19th in the Championship table but are now six points clear of the relegation places.