i have flown 5 times from ORD MAD ORD in the last 7 months. i have experinced bidding and also upgrading when it is offered while checking in 24 hours in advance.
i dont know the strategy when they offer one or the other. i have bid and lost it then was able to upgrade the day of departure at Barajas or Ohare.
At ohare they charge 400 Euros. last week at Barajas i paid 499.99 Euros.
considering i paid 1100 USD for my fare i think its worth it. Especially when you are flying to MAD from US. it helps to get a lie flat seat. also the business class lounge benefits are great. if you take advantage of it. Pretty Good breakfast in MAD and the use of showers come in handy. the lounge at Ohare is not a big deal. MAD is nice. i prefer the lounge at 4S, much better breakfast than Terminal 4.
Good luck. let me know if you have any more questions on this subject.