Hey Pannill, is it a mountain bike or a road bike?
I bought a few nice mountain bikes here for my gal and I on her birthday (May 1st

)last year and we love them. I ride just about anywhere although it is uncomfortable on the busy streets. I love riding in the parks and near the Royal Palace as well as in the old parts of the city where there are cobblestone streets and less cars.
I never, ever lock the bike up and leave it outside though, NO WAY! It would not last an hour.
There is mega bike/scooter theft here and it is a bad idea to leave a nice bike outside.
We store our bikes in the spare bedroom of our apartment and that works great. It is a hike to get them up the stairs (4th floor walk-up that seems more like 8 floors

) but it is a much better option to leaving them in the street, no matter how well they are locked up.
Bring the nice one if you like but plan on keeping it in your room. Maybe you can bring a few of those bike hooks from home or a rack made for the wall and hang it in your room.
I know yo ucan check the bike (in a box) as one of the 2 suitcases allowed on a ticket.
The streets of Madrid are not bike friendly in the least, no bike lanes at all but many are trying to change that. On the other hand, there are many parks and open spaces that are very inviting to cyclists.
I say bring it!
You have a riding partner in me if you want
Saludos,
jer...