50 minute connection in Madrid for local flights...is this enough?

I'm not that familiar with Madrid airport either, but have you considered a direct flight to Bilbao instead? That would probably be my choice.

I agree fly to Bilbao. Take the bus from there.

Madrid airport is huge! 50 minutes would be very risky for a transfer. Take a direct flight to Bilbao.

Consider that boarding for the connecting flight will begin 30 minutes before departure, leaving you essentially 20 minutes to get off the first flight and make your way to the new gate. If both gates are in the same terminal you might be ok if you can get off the first flight quickly. Walking between terminals 2 and 4 will take about 20 minutes. I’m not certain if the intra-Europe and intra-Spain flights arrive and depart from the same terminal. If your originating flight departs late, or there is a delay after landing getting to the gate, you’ll probably miss the connecting flight. If you’re changing airlines you’ll probably be using a different terminal. For me, that’s too tight of a connection.

Try plugging the flights into the airline website(s) about the time one is landing and the other is taking off. It should let you know which gate the originating flight is going to, and the gate the departing flight is leaving from. You can then look at the Madrid airport map to see how close the gates are. While the gates change, they should remain pretty much in the same area of the airport.

We just flew through on Iberia Air from Granada to Paris, with a 1 hr 15 minute connection in Madrid. Our flights landed and took off from the same terminal (4). The terminal is HUGE. We walked fast for at least 15 minutes to get from gate 80-something to 40-something. They were boarding when we arrived. We had to get on buses, which took us to the plane on the tarmac. Then wait in line again to walk up the stairs to the plane. 50 minutes might have been enough time, but if we needed to change terminals I don’t think we would have made it.