This is interesting isn't it? I read scores the same way I do novels, and for similar reasons - entertainment etc.
And yes I can 'hear' how the piece goes in my mind. It kind of came naturally to me - I've been around music so long, that I don't remember specifically 'learning' it or deliberately 'teaching' myself to do it.
But here's something else you can do away from the piano, that is sort of a carry on of what Bernhard is suggesting, and that is practise sight singing. Are you cringing? I don't know if you like singing commelevent, but usually people who have an 'ear' for music, are pretty good at it.
Like Bernhard said, start with easy pieces. I like to write my own exercises and encourage students to also write their own singing exercises. Like Bernhard mentioned with learning how to read, first, you have to establish foundations.
Here's an exercise you can try if you like (away from the piano of course) I'm also assuming you haven't done sight singing before. If you have and you're an expert, just humour me.

1. Start with C major scale. It's easy (and easy to explain in a post too

) On manuscript using treble clef, write CDEFG. For now, don't worry about note values. Just work on pitch first, add values later. So, use semibreves to write your notes.
2. Now, sing or hum the notes, keeping your eye on the note as you sing them.
3. With this combination of notes, and using steps only - this is really important when you're first training your brain (which is what you're doing, so it can send the correct signal to the muscles so they know how to tighten your vocal folds) write on your manuscript - eg, CDEFEFGFEDCDEDEFEFGFGFD. In other words, steps going up and down, but always connected. (Add thirds, fourths etc later)
4. Sing your notes.
5. When you've had enough of this, now add values. In essence you are writing your own melodies. You can write in simple quadruple, compound duple, simple triple - anything. In fact, the more varied exercises you write for yourself, the more practise you're giving your brain, the easier it will be. It will also be easier for you to 'hear' music like what Bernhard is talking about. Just remember to keep these melodies in steps to begin with.
6. Now add the rest of the scale i.e. ABC. Repeat a similar process.
Give yourself at least two weeks every day practising this easy level before you add larger intervals. Start with thirds. Be patient. Add fourths, etc.
This will keep you well and truly busy away from the piano, and will also benefit your musicality, and will help your sight reading skills for the piano.
I suggested treble, but you can do the exact same with bass.
Oh, it also doesn't matter that your singing 'C' is is not concert pitch. It's the interval patterns that matter.
Hey commelevent, I hope you have fun! Heee heee
