Mike:
I don't think this is as much an ear exercise as one in math. For sure the correction tuning has to do with your ear. However, the "mystery" of transposition is really just a mathematical formula.
I suggest you sit down with your trumpet player friend and both play what is called a "Bb concert scale". The term concert means the "real" pitch an instrument makes. Both the trumpet and alto sax are transposing instruments. If you look on your music it will say Eb alto saxophone. His or her trumpet music will say Bb trumpet. What this means is when the instrument in question plays the written note "C", that is the note that should come out. Therefore, when the alto plays a written "C", it is actually an Eb and the trumpet "C" is really a Bb.
Beginning ensembles often play music in the key of Bb "concert". This makes it easier for a variety of transposing instruments to play with a minimum of notes altered by the key signature. Your (alto) Bb concert scale is written as a G major scale (with one sharp). His or her trumpet scale will be written as a C scale. This change in the written notes will allow the two of you to play different written scales that will sound the same. An instrument that does not transpose (like a flute) will be playing the actual Bb scale with two flats.
Sit beside the trumpet player and compare "notes". When you play a G, he or she will play a C.
alto G scale (really Bb concert): G A B C D E F# G
tpt C scale (really Bb concert): C D E F G A B C
Rather than comparing first to the trumpet, it may be more useful to compare to a concert pitch instrument like a flute or piano. Notice that your pitches must be six notes higher in the scale in order to match. When they play Bb, you play G. The trumpet transposition is much easier, they just play it up a tone. If the flute plays Bb, they play up one tone to C.
I don't know your knowledge of key signatures or if you understand major and minor intervals. Hopefully, this information can give you a starting point to figure this thing out.