Transposition

It sounds like you are changing key from a concert C instrument to a concert B-flat instrument. Once you change the key signature, select the entire line of music and press ctrl-down arrow. This will move it down 8 steps. If this is the only instrument you can click outside of a staff to deselect everything. If there are other instruments you need to select the entire staff once again. In the notes->Transpose... menu make sure "By Interval" and Transpose key signature" are checked. Select the down button near beneath "By interval" and change the drop down menu to the right of that to "Major Second" this will transpose the notes down another step and fix the key signature.

Another thought that may make it easier. Since you are changing instrument, you can right click in a measure where there are no note and select staff properties. To the left of the middle is a button that says "Change Instrument" you can press that to change the instrument to the one you want. After that you will need to select the entire staff and press ctrl-down arrow to transpose it down an octave and put in the correct clef.

Changing Clef doesn't transpose any notes.*1 (The name of the note and octave of the note, remains the same)
You don't need to select all. Just put the new Clef.
If the new notes are too high or too low (If many of them are on ledger lines) : Select, and change the octave with Ctrl + Up/Down arrow.

*1 After changing the Clef, it is not a correct point of view to calculate this change according to the old Clef and to think that the notes are transposed.

Changing the clef should automatically alter the key signature to match. Perhaps you accidentally added the wrong clef - there are clefs that look like bass clef but if you look more closely you will see they are on different lines.

Anyhow, the basic steps for changing from treble to bass should be more or less the same as you described for Sibelius:

1) Change the clef, by dragging it from the palette or by selecting the first measure and double clicking the clef in the palette. As mentioned, this automatically updates the key signature to match the clef.

2) To transpose the notes down an octave exactly, easiest is to Ctrl+A to select all then press Ctrl+Down.

However, if as mentioned you actually want to transpose not just an octave but a ninth - to change the key as well, like to play music written for Bb clarinet on a C instrument like the cello - then as mentioned, you should use Staff Properties / Change Instrument, so that the transposition is handled correctly.

If you continue to have problems, please attach your score and describe what you want to do in more detail, then we can provide better help.

If the music you have is written for a Bb instrument and you want to, say, play the trombone in Bass Clef at orchestral pitch, then enter it using one of the Bb instruments (cornet, trumpet, clarinet) and then change instrument to trombone. As above, [Ctrl] a followed by [Ctrl] arrow to change octaves.