Instead of writing a flat sign before every Bb note, it is easier to write just one flat sign after the treble clef. This means that all B notes on the staff are played as Bb, even though there is no flat sign placed before the note. This is called a Key Signature. See page 45 for more information on key signatures.
This duet uses a key signature, which tells you to play all B notes as Bb. To play duets well, you need to be able to listen to yourself and the other player at the same time. Learn your part well and then try listening to both parts as you play.
Sometimes it takes only two or three notes to create a good saxophone part for a song. In a song like this, where and how the notes are played is the most important thing.