Well, first, I suspect that the order to return immediately would have precluded Bartimaeus from simply putting the amulet down and then picking it up again. This was undoubtedly the point, since Nathaniel is known to be fairly careful with his phrasing.
The part about “awaiting further instructions” would presumably preclude Bartimaeus from simply going right back, or indeed doing anything else he might want to do, as we see from the fact that Bartimaeus does indeed follow Nathaniel around:
With that, my assignment was complete. All that remained was to return
to the boy. I exited cupboard and study without any hiccups and set
off back upstairs. This was where it got interesting.
I was heading up to the attic room again, of course, using the sloping
ceiling above the stairs, when unexpectedly the boy passed me coming
down. He was trailing in the wake of the magician’s wife, looking
thoroughly fed up. Evidently he had just been summoned from his room.
I perked up at once. This was bad for him, and I could see from his
face that he realized it too. He knew I was loose, somewhere nearby.
He knew I would be coming back, that my charge had been to return to
him immediately, silent and unseen, to await further instructions. He knew I might therefore be following him now, listening and watching, learning more about him, and that he couldn’t do anything about it until he got back to his room and stood again within the pentacle.
The Amulet of Samarkand
We see that both Bartimaeus and Nathaniel have basically the understanding of Nathaniel’s instructions that I outlined above.
Now, could Bartimaeus have simply disobeyed Nathaniel’s orders, while carrying the Amulet, in the hopes that it would protect him from the Shriveling Fire? Possibly. But, assuming the possibility occurred to Bartimaeus, why would he take this risk? The Amulet is designed to protect magicians against external attack, not to protect spirits against (internally-originating) penalties related to their enslavement. Would Bartimaeus really want to risk his very continued existence for the mere possibility that he would be able to torment or kill Nathaniel without penalty? He bears a great deal of antipathy toward his masters, sure, but not enough to risk his own essence.
But perhaps more important, I don’t think the Amulet would have protected Bartimaeus from the most useful spell Nathaniel could have used: the Dismissal. There’s no doubt that the Amulet would have absorbed the attacks mentioned in the question, and perhaps even the Indefinite Confinement. However, the Dismissal is not really an attack, and would probably not be recognized by the Amulet as harmful (quite the opposite). Moreover, the Dismissal merely breaks a spell that already exists (namely, that binding the spirit to the material world in the first place), and doesn’t produce any new magical effect, so it’s doubtful whether it even “counts.” Once Nathaniel had dismissed Bartimaeus, he could merely pick up the Amulet.