Transponse playback

If you create a new score and use "Select instruments" from.the wizard to use Bb Trumpet and make sure that the Concert pitch button is not selected, then you can enter the notes as you would expect to see them in your part and Musescore will take care of the transposition. They will sound a major 2nd lower on playback.

If you have already entered the notes but have used a non-transposing instrument (for example by selecting the treble clef template during score set up) all is not lost. First, get the instrument right by right clicking on the stave and in Stave properties change the instrument to Bb Trumpet. You will see the notes have now been moved up a major 2nd, so put them where they belong by selecting everything using CTRL+A and then pressing down arrow twice.

You may find it useful to read these bits of the handbook.

https://musescore.org/en/handbook/3/create-new-score#instruments-and-vo…
https://musescore.org/en/handbook/3/transposition

On the music sheet for a musician, a trumpet (in Bb?) and a horn (in F?) do not have the same key signature.
For example, if a score is written in C major, the F-horn is notated in G major and the Bb-trumpet in D major.
Do not use the concert pitch when only transcribing an existing score because the sheet is already correctly notated for the instruments. .

When you compose a score, it can be helpful to switch to the concert pitch. Then you see the notes as they sound, and it's easier to set a chord. Both instruments then have the same key signature.
When you are done switch off the concert pitch button. You may then export or print the sheets for trumpet and horn in the correct key signature for the musicians.