All three suspensions will begin at the start of each player's Minor League seasons.
Bickford, the club's No. 5 prospect per MLBPipeline.com, is on the roster of the Class A Advanced Carolina Mudcats. The right-hander was acquired by Milwaukee from San Francisco as part of last season's trade for Will Smith.
Soltis is currently on the roster of the Class A Greensboro Grasshoppers, while Loficial is a member of the Rookie-level Dominican Summer League Blue Jays roster.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.