Murasama blade was described by Wolverine as "the only thing in the world that could put him down." as it cuts his skin at molecular level. If we harness a bullet out of the blade and shoot Wolverine will he die?
In answering this we need to make a few assumptions:
First I'm assuming you're referring to the second of the two blades; the blade forged with Wolverine's own soul not the one containing a fragment of Muramasa's soul. That first blade (the black blade) whilst much stronger than a normal sword, drove you mad and doesn't seem to have any effect on healing factors.
And secondly, from the fact Daken was able to have a claw made for him form a fragment of Wolverine's Muramasa blade, we assume that we can turn the sword into a bullet without destroying it's essence.
It's worth noting here that I think, from what I've read, the amazing cutting power and the negation of a mutant's healing factor are separate powers of the blade and come from separate sources. If this weren't the case I'd assume that turning the blade into a blunt object, like a bullet would negate it's healing factor negating abilities.
So we now have a bullet with all of the aggravated damage (to take a phrase from a popular RPG) and none of the cutting ability of the blade. That's ok, I'm pretty sure the blade couldn't cut through adamantium:
Quoting Thaddeus, an authority on Marvel Comics:
Adamantium is proof against any kind of energy, matter or attack once it has been set into its final form. It takes the powers of Omega level mutants (like Magneto), Asgardian gods like Odin, or cosmic beings like the Silver Surfer or Thanos to change or deform it after it has been set. The Muramasa Blade not need to do anything but sever Logan's vertebra which are not magically connected with Adamantium allowing for them to be separated without molecular matter' slicing powers to be used.
So this bullet could kill Wolverine, but you'd need to make your shot count. A shot to the heart might put him down for several weeks as the tissue slowly healed; Wolverine can survive without oxygen indefinitely so deoxygenating his blood wouldn't do much permanent damage. You haven't stopped the rest of him from regenerating.
Shooting him in the brain would work, but you'd either need to put the bullet through his eye socket, or at the right angle through his nose, under his chin etc, as you still can't pass though his adamantium skeleton. This would likely wipe his memory (again), and take him down but I don't know if it would kill him off. He's regenerated from a single cell, a brain cell so it wouldn't finish him off, he would just take a long time to recover, and have a bullet with a piece of his soul in it in his brain. Interesting.
Your best bet would be to try and sever his head by shooting at his neck and hoping to destroy the soft cartilage between vertebrae. But it's long shot.
In short yes, maybe it could, but you'd need the perfect shot. I'd stick with the sword.