Bernard, yes, there is a Bb trombone, in fact it's probably the most prevalent of all trombones. I miswrote when referring to clarinets, trumpets, etc., as "true" Bb instruments. The Bb trombone and BBb tuba are just as truly Bb instruments. The difference is that music for clarinet et al is transposed up a full tone whereas that for trombone and tuba is not.

Now, to reading sheet music: if a trombonist were reading treble clef music written for clarinet or trumpet, s/he would need to transpose an octave plus one full tone down. But if reading treble clef music for flute or oboe, no transposition would be needed other than the octave shift.

As to the key of sheet music. It's written in whatever key the composer intended and to refer to sheet music written at concert pitch as in "C" is incorrect. It may be in C,D,E or whatever, but when a non-transposing instrument plays from such music, the pitch comes out as written.

To further muddy the waters, we can throw in "oddball" clefs. While most of us are familiar with the G (treble) and F (bass) clefs, there is also the C clef, which is particularly familiar to viola players. The G clef places the G above middle C on the second line (from the bottom) of the staff by centering the body of a stylized G on that line. Likewise the bass clef consists of a stylized F with the crossbars (the two dots) centered on the fourth line of the staff (F below middle C). The C clef is a stylized C with its center usually placing middle C on the middle line of the staff. All these clefs can move up and down on the staff to give notes different positions but, in practice, the C clef is placed differently far more frequently than the other two.