Originally Posted by
Reifel
You will arrive at T1 (or T2, not sure, but doesn't make any difference anyway). From there it is really a trek to T4, there is a landside bus connecting the terminals which takes at least 15 minutes IIRC. Furthermore you could take the subway, again landside.
It is reported that there is a airside bus, especially for good use for nonschengen passengers which hold no Schengen Visa, and therefore need to connect airside. Maybe someone else can enlight.
But since you need to enter Schengen in MAD anyway, I believe you will pass immigration in T1/2 arrivals (get your bags there if not checked through, but your status may help to get this solved at check in in the US). Then you take airside bus or metro to T4. And then you collect your IB boarding pass at the regular check in area (and redrop your bags there). I don't think that UA can issue boarding passes for IB at your first departure point. Then you pass regular security. 3 hours seem ok to me, but again it's quite a trek. If you have time in T4 you can use the Iberia lounge.
Maybe someone else can enlight if a Nonschengen to Schengen traveller is entitled to use this mysterious airside transfer bus
Here's the link to the airport's page on the shuttle bus.
The airside bus doesn't seem to apply in this case (it seems to be for transfers within non-Schengen or Schengen flights).
You should take the (free) landside bus from T1 or T2 to T4 from the departures floor (exit baggage claim and go upstairs).
You could take the metro, but that would be very costly (I'd only consider it if I had a transport pass).
3 hours should be fine, good luck with your trip!