Many of the books put out for the trumpet are just taken from the score for instruments in C such as piano scores. The book you bought was not transcribed for B flat trumpet. I believe if they sell a Disney songbook for trumpet, you should be able to play along with the Disney recording. Sure, you can play the melody from this book, but try to play it with a Youtube recording and you are flat by a whole step. I did check on Amazon. If a flute player bought the same book, you could play together, but you both could not play with the original recording for the movie.
When a director says, “Play a concert B flat.” A trumpet player plays their C because, what is called a C on the trumpet, matches a B flat played on a piano. John is correct.
Trumpeters in orchestras learn to transpose in their heads. Your software correctly transposed the correct key signature. Music that is written in the Key of F for an instrument in C should be transposed to the Key of G for the trumpet player. The software however did not change the notes. It should be G (OOO) F# (OXO) G (OOO) E (XXO) F# (OXO) G (OOO). I’ll bet the software could get it right, but something went wrong in using it or the software is flawed.
Here is a link to the piano score. https://i.pinimg.com/originals/a4/3e/ce/a43ecec101b69718a8047387fb2096d8.gif
You can see the book you bought did not transcribe the part for the trumpet based on the movie music.
If you just want to play the melody on your horn and do not care to play along with the recorded music, play it without transposing. Play F (1) E (1,2) F (1) D (1,3) etc…
If your friends bought the same book, they will be able to play the melodies together. I checked flute, alto sax, and trumpet books. So no worries.