A partial indulgence commutes only a certain portion of the penalty; and this portion is determined in accordance with the penitential discipline of the early Church. To say that an indulgence of so many days or years is granted means that it cancels an amount of purgatorial punishment equivalent to that which would have been remitted, in the sight of God, by the performance of so many days or years of the ancient canonical penance. Here, evidently, the reckoning makes no claim to absolute exactness; it has only a relative value.God alone knows what penalty remains to be paid and what its precise amount is in severity and duration. Finally, some indulgences are granted in behalf of the living only, while others may be applied in behalf of the souls departed. It should be noted, however, that the application has not the same significance in both cases. The Church in granting an indulgence to the living exercises her jurisdiction; over the dead she has no jurisdiction and therefore makes the indulgence available for them by way of suffrage (per modum suffragii), i.e. she petitions God to accept these works of satisfaction and in consideration thereof to mitigate or shorten the sufferings of the souls in Purgatory.
(Indulgences, scroll to VARIOUS KINDS OF INDULGENCES)
Let's keep in mind a few guardrails for our discussion of the Sabbatine Priviledge.
1. There is no time or space in Purgatory.
2. Only dead saints are there.
3. There are no clocks, watches, daytimers, calendars or organizers in Purgatory.
There is no Saturday in Purgatory (see above). Saturdays only occur for the living. Note that the Bull says, "especially on Saturdays, the day consecrated by the Church to the Blessed Virgin."
Read in context the Bull underlines Mary's constant intercession for the faithfully departed and our immitation of her faithfulness not some magic formula to spring souls on Saturday.
And that's no bull.
"The name Sabbatine Privilege is derived from the apocryphal Bull "Sacratissimo uti culmine" of John XXII, 3 March, 1322."
The apocryphal Bull is bull, BTW, I'm not sure if I made that clear. Pope John XXII never wrote such a document.