I play Rumble and want to use item that buff me when my shield is turned on.
Which items can I purchase to make my shield more potent?
Ardent Censer, Mikael's Crucible, Shurelya's Reverie, and Redemption all increase shield strength. However, they all share the same unique passive, which means they don't stack if you have more than one of them. Revitalize is a rune in the resolve tree that also buffs shielding.
I will add, however, that none of these items are good on Rumble and the playing for shield strength vs. raw damage will net you little benefit. I recommend checking out sites like u.gg and leagueofgraphs to find what item builds and runes are working best for your champion on the current patch.
In addition to the other answer, Rumble's shield does scale with AP. Simply building more ability power will increase the magnitude of your shield without needing to build potentially odd items that aren't fit for your champion.
You can also build more ability haste (CDR) to reduce the cooldown on Rumble's shield, but I will note that currently, Rumble's most meta build of Hextech Rocketbelt -> Shadowflame -> Rabadon's Deathcap + Zhonya's Hourglass is quite low on ability haste in comparison to other AP-building champions. Take that information as you will.