id say you got a scope problem since it wont even hold a group.

ditch the BSA. get good bases and rings and a better scope and i bet it will atleast group.

i know good scopes are pricey..alot more pricey than a BSA..but if you want your gun to shoot, and it wont with a low end scope, a higher end scope will usually help. not saying you need to spend a grand on a scope, but id atleast go mid range for my deer gun..Nikon, burris, leupold etc...their lower powered scope prices arent too steep...but still looking at 100-200$ id say...

good luck...cant say for sure thats your problem..but if you shot 3 differnt kinds of ammo and know the rings and bases are tight, then id have to say scope problem