They went ahead inside two minutes through Karl Duguid, whose low shot from Kayode Odejayi’s pass deflected in off Bury left-back Joe Skarz.
Anthony Wordsworth forced Cameron Belford into a good save and Duguid missed a good chance before Ian Henderson increased the lead in the 19th minute when he brilliantly headed in from Wordsworth’s cross.
Colchester keeper Ben Williams saved Michael Jones’ first-time shot before the hosts hit a third on the half-hour when Duguid calmly slotted in from Wordsworth’s pass.
Williams denied Bury substitute David Worrall and Andy Bishop headed over from Skarz’s cross for the visitors early in the second half. But Colchester went further ahead after 64 minutes through Lloyd James’ stunning 30-yard free-kick.
Substitute Lenell John-Lewis fired in from close range for Bury in the final minute but it proved only to be a consolation.