Bullard, sidelined since early October with knee ligament damage, was introduced in the second half with his side leading 2-0 thanks to a first-half double from striker Jay Simpson.
Blades forward Ched Evans then scored twice as the Blades, booed off by sections of their home support at half-time, staged a brave second-half fightback.
Simpson, who ended his season-long goal drought last week with both goals in Hull's 2-0 home win over Bristol City, opened the scoring in the third minute and converted a penalty in first-half stoppage time.
Evans pulled one back for United in the 62nd minute and fired an equaliser 11 minutes later, but Bullard, in only his fifth appearance of the season, converted another cross from on-loan Manchester United midfielder Cameron Stewart, who also set up both Simpson's goals, in the 93rd minute.
Source: PA
Source: PA