The Reds had knocked in 10 goals in seeing off Chester FC and Tranmere Rovers in their first two summer friendlies, while the hosts had shipped the same number of goals without a response against Rangers and Huddersfield Town.
There was little between the teams on this occasion, though, with Liverpool too often failing when it came to the final ball and Bury rather comfortably holding their Premier League opponents to a draw.
Some good defending then prevented Bury from falling behind, as Adam Thompson blocked Sheyi Ojo's goalbound shot in front of goal, before the same player had a curler kept off the line by Eoghan O'Connell.
The Shakers' only opportunity in the opening 45 minutes was wasted by new recruit Gold Omotayo following a poor backpass from Alberto Moreno, with a bad first touch denying the Bury striker a chance to tap the ball into the net with Loris Karius stranded.
Liverpool, as they have done in their previous two summer friendlies, changed their entire outfield lineup for the second half.
Bury ensured that Liverpool would not have things all their own way, though, and they nearly snatched a goal when Ryan Cooney's shot from a tight angle clipped the outside of the upright.
BURY (4-2-3-1): Murphy (Hudson 75'); McFadzean (Moore 67'), Cooney, Thompson, O'Connell (Shotton 72'); Mayor (Whelan 67'), Dagnall (Archer 62'); Aimson, Danns (Adams 66'), Styles (Dawson 46'); Omotayo (Bunn 62')
LIVERPOOL (4-3-3): Karius (Grabara 62'); Clyne (Camacho 46'), Van Dijk (Klavan 46'), Matip (Gomez 46'), Moreno (Robertson 46'); Milner (Lallana 46'), Fabinho (Keita 46'), Jones (Chirivella 46'); Ojo (Woodburn 46'), Origi (Phillips 46'), Sturridge (Solanke 46')