It would depend on how the damage you receive from Bond of Stone is calculated. There are four possibilities for how it could work. (I'm using 10% as the reduction for BoS, since it makes the numbers nicer.) In this situation, there's a Sion and a Thresh, both with BoS, and Sion is hit by a Jinx rocket for 1000 damage.
SCENARIO 1: Armor is applied before BoS, which is dealt as normal true damage (since it doesn't mention a damage type).
1000 incoming physical damage to Sion -> Armor applies, 500 incoming physical damage to Sion -> Sion's BoS applies, 450 incoming physical damage to Sion -> Thresh's BoS applies, 405 physical damage to Sion, 45 true damage to Thresh. This damage is dealt, Sion takes 405 damage and Thresh takes 45. When Thresh takes 45 damage, Sion's BoS triggers again, and he absorbs 4.5 of the damage. This continues until League just rounds it off; the final result is that Sion takes 409 damage and Thresh takes 41.
SCENARIO 2: Armor is applied before BoS, which is dealt as a health cost (does not trigger iterated BoS).
1000 incoming physical damage to Sion -> Armor applies, 500 incoming physical damage to Sion -> Sion's BoS applies, 450 incoming physical damage to Sion -> Thresh's BoS applies, 405 incoming physical damage to Sion, 45 true damage to Thresh. This damage is dealt, Sion takes 405 damage and Thresh takes 45.
SCENARIO 3: BoS is applied before armor, and deals normal true damage.
1000 incoming damage to Sion -> Thresh's BoS applies, 900 incoming physical damage to Sion, 100 incoming true damage to Thresh -> Sion's BoS applies, 810 incoming physical damage to Sion -> Armor applies, 405 incoming physical damage to Sion, still 100 incoming true damage to Thresh. This damage is dealt; Sion takes 405 and Thresh takes 100. When Thresh takes the true damage, Sion's BoS applies again, and he absorbs 10 of the damage. This continues until League rounds off; the final result is that Sion takes 414 damage and Thresh takes 91.
SCENARIO 4: BoS is applied before armor, and is treated as a health cost (does not trigger iterated BoS).
1000 incoming damage to Sion -> Thresh's BoS applies, 900 incoming physical damage to Sion, 100 incoming true damage to Thresh -> Sion's BoS applies, 810 incoming physical damage to Sion -> Armor applies, 405 incoming physical damage to Sion, still 100 incoming true damage to Thresh. This damage is dealt; Sion takes 405 and Thresh takes 100.
If I had to guess which one is true, I'd say that scenario 2 seems most likely, since it's the most obvious how much damage you can expect to give and take with that setup.