I have cleaned the weapon and can only get it to fire one shot at a time.  The problem is when the first shot is fired the gun cycles and ejects the spent case and pickes up a fresh one, but the hammer is not cocked.  When i cycle it by hand it cocks the hammer and is ready for another shot.  Yes it hold the bolt open on the last round.  Any ideas  Thanks.  Bushmaster lower with a 16" patrolman upper.  Another thing the bolt is  not a conpletely encircled at the rear.  The bottom half is cut away.  So it is just a the top half thats there.  Thats the bolt that the gun came with.  

Is the hammer down on a live round? If so, then it sounds like your disconnector is not catching the hammer and holding it back.

Function check your UNLOADED rifle. Charge the weapon WHILE holding back the trigger. Without releasing the trigger, the hammer should be held by the disconnector. Upon releasing the hammer, it should lightly click as the disconnector releases it and the trigger catches it. Pressing the trigger now should cause the hammer to fall.

Will the bolt lock back on an empty mag each and every time? It could be shortstroking, but still lock the bolt back now and then.

As for your bolt carrier, it sounds like a Colt Sporter bolt carrier. It is made that without the lower rear portion, so that is normal.

I have  had that problem twice.  In both cases, the hammer was hitting the disconnector when the bolt slammed the hammer back.  In one case, the buffer was way too light, so I replaced it, and everything was fine.  The second time, it was an M16 hammer I was using.  I switched to a semi-hammer, and it still did it until I ground some of the hammer head away.  Check the back of the disconnector to see it the hammer is striking it.  A weak recoil spring could cause excessive bolt velocity too.