Presumably, the ring never left the top of the Stairs. The whole leaving/being sent back business took place on the spiritual level. Gandalf was resurrected into the body which was lying on top to the mountain, sword, staff, ring and all.
Yes, there is the passage about "naked I was sent back into the world", but I always thought of it as figure of speech, stating his spiritual position rather than corporeal one - otherwise,
A) the imposed restrictions of travel in bodily form apply
B) no reason to come back to the inconvenient place on top of some mountain (with the possibility of the reason being the wish to pick up his stuff, of course
)
C) in coming back on top ot the mountain, he would be exposed to the unpleasant view of his own previous body lying up there