I think you've got it backwards.

If a Bb instrument plays a C it sounds the same pitch as the Bb on a C instrument. To sound like a C, the Bb instrument's music must tell him/her to play a D.

You need to notate the music for the Bb instrument 1 full tone (two semitones) higher than what is shown on the C instruments' music. The key signature for the Bb instrument will have two sharps more (or two flats fewer) than the notation for the C instruments.

If you (C instruments) read and play in G, the Bb instrument must play from music notated in A.

I've never seen a Bb trombone, but won't argue that they don't exist. The "classical" trombone is in C, but plays from dots notated on a Bass Clef. If a "normal" trombone player reads from the treble clef notation for an Eb instrument, but "adds three sharps" and merely changes the treble "Fancy S" sign to the bass "backward C" the notes played will sound the same as C instruments playing from "C instrument notation."

In the 50s it was common to find "Combo Books" with identical tunes in separate books for C, Bb, and Eb instruments, and the usual "solution" to the absence of decent bass clef parts in the C book was to give the 'bone player the Eb book.

John