Having already beaten Shrewsbury in round one, the Blue Square North side showed no fears and had the better of a grim first-half.
Alex Gildea had a shot saved from 20 yards and a cross from Rob Dale flashed invitingly across the face of the Bournemouth goal.
But after the break League Two Bournemouth piled on the pressure and several times came close to preventing themselves a 372 mile journey for the replay.
Bell, who had little to do before the 60th minute, was then obliged to dive to his right to keep out a fierce shot from Lee Bradbury destined for the corner of the net.
But Bell made his best save in the 88th minute when a close-range header from Bradbury was somehow pushed to safety by the goalkeeper. Blyth had few opportunities to test Shwan Jalal in the second-half but held on for the final whistle when they raced across to receive the acclaim of their 300 travelling fans.