Peter, have you tried using the Auto Hide for the Task Bar. You can have the Task Bar Locked & have Auto Hide set as well & the Task Bar will Auto Hide.

Experiential with the settings & see how what suits you. If you want Auto Hide you have to set it.

The fact that the Task Bar hides in Firefox & IE is not really related to what happens in Word.

If you have the Task Bar Locked it will always show irrespective of what program you are using.

If you set it to Auto Hide it will only show when you move the mouse pointer over it, also irrespective of what program you are using.

If don't select any of these features for the Task Bar it will behave much as you have described, showing in some programs & not others.