Irelia is so farm dependent, and Rumble just shuts down her farm. You can either tower-hug and end your lane with 2 CS, or you can feed mercilessly trying to get farm.

What do I do, all ye noble seers of light and truth? How do I lane against Rumble as Irelia?

I toss on gp5 quints, and actively gank rumble... that's really all, and if you need to cs, blade surge the last hits and equilibrium stun him before he harasses you. MR never hurts either, especially wits end vs him