What model of Bushnell scope came with the rifle? Sportsman, Banner, Trophy or...? They used to come with a Simmons 8-point. I have had no issues with the bases that came with mine (or the scope though it is low quality), but I eventually swapped out the scope for a Bushnell 3200 series and the rings for Weaver Grand Slams . The same scope can often be found on the EE for $200 or so, the rings were around $25 or so, new Weaver bases would run you around $20 if you choose to replace those as well. For what its worth the scope (and rings and bases) were on mine for around 160 or so rounds of 7mm Rem mag with no issues. The scope is now on a Mauser 98 in 9.3x57 with no issues so far, but its sitting in quick release rings and that rifle has iron sights for backup.
Jim