Yep, that’s generally it. Had Joseph of Arimathia or someone else not asked for Jesus body it would have been thrown on a trash heap or buried in a shallow unmarked grave, which was the lot of the poor and those executed.
Note that in the Story of Lazarus being raised from the dead, he was in a cave that was made into a tomb.
The disciples hastily laid Jesus in the tomb, placed coins on his eyes to keep them closed, covered his face in a manner similar to Arab Islamic burial customs, wrapped his body in a linen cloth, placed some of the flowers and spices they had on hand untop of the body and then took off to make it back to the city before sunset.
The women came back on Sunday morning for two reasons…to finish the funeral prep of Jesus body, and to make sure he was dead…it was the custom back then to check on the deceased within two or three days to make sure they were really dead.