Sibelius doesn't know about Bombardons, but the important thing is to look at what follows the instrument name, e.g. "in Es" or "in Bes", which mean respectively "in E flat" or "in B flat".
In the snippet below, all three instruments are sounding a concert C. Double bass is non-transposing. E flat bass performs A natural to sound a concert C, and B flat bass performs D natural to sound a concert C.
So if you read the B flat bass part and transpose down a tone you get concert pitch. And read the E flat bass part, transpose up a minor third to get to concert pitch.
British Brass Band has B flat and E flat basses but written in treble clef. Only bass trombone is written in bass clef, and that's at concert pitch. I've not come across transposing bass clef parts like these before.
Here are some staves that show the notes the various brass band instruments perform and the corresponding sounding concert pitches: