You would likely be able to build a partial or complete bolt with parts from Gun Shack, Sharp Shooter Supply, Numrich, Brownells, Midway USA or similar.
Sadly, that doesn't mean it was done correctly. The reason for trigger/safety mechanism being suspect vs the bolt is that your firing pin is held back by the same piece of metal that acts as the bolt release lever. Basically, the only thing that can let the firing pin go is related to the trigger or safety. The trigger sear engagement is responsible for holding the lever (can be seen inside the action near the rear on the ejection side) which then holds that round knob on the side of your bolt. Nothing in your bolt keeps the firing pin held back once you rotate your knob down in the final step of chambering a round -- that lever on the side is responsible for holding the loaded firing pin back. It needs to hold it back until you pull the trigger with the safety off. My guess is that the trigger is out of adjustment (if it's an adjustable kind) or maybe is a bad mix of Savage parts from different models or generations (I'm spitballing there).
More questions:
Did savage install the trigger at the factory and test it, or did they just mail the parts out?
Does this problem occur when the safety is on?
What style trigger do you have?
If you hold UP on the bolt release lever (takes some strength) while you close the bolt, will the pin stay cocked until you let it go?