I don't have
experience with creeping bellflower specifically but I have composted some very invasive weeds with no problem, even though most local people burn it or send it to landfill. If you know how it usually spreads and do things to prevent it from spreading that way, and you are okay with the 1% risk of having to weed an area where it survives anyway (ideally a spot already infected by the weed, maybe the area where you pulled it up originally), then I don't see why not.
The area where I live is under constant assault of scotch broom, which I
chop down at ground level before it goes to seed and use for mulch/compost on my property, which is already covered in decades of dormant scotch broom seed ready to pop up as soon as the soil is disturbed. I have dragged around big piles of this stuff and in 2 years I've only seen 2 new plants pop up on my property, and they're easy
enough to kill. The only catch is that I actually do have to check my property and take out those new plants before
they go to seed, but I was going to do that anyway.
Google says creeping bellflower spreads by seeds and runners. I've dealt with aggressive runnering plants in the past by chopping them up really small and sticking them in a
bucket for a few months until I'm sure they're good and dead before adding to compost. No promises that it will work for the bellflower but it's what I would try.