It is a serious invasive species and you are right it is everywhere. It can only be killed by excluding light for 2 years so leave the plastic on or use  a brush killer like Roundup. I cut it off at about 6 inches and immediately treat the cut stem and remaining leaves with Roundup to kill the extensive root system. It has a huge root that can go down 16 inches. If the roots aren’t completely dug out it comes back, fast. There will always be bellflower but eradicating it does a lot of good and the amount that comes back is less than 10% . The first year  is the most work and the next 2 less but more than maintenance because of the number of seeds in the ground have to sprout and be killed. If your weeders are only pulling it they aren’t getting the main roots. 
I don’t want to use chemicals and only use Roundup on bellflower and thistles. I also use only enough to kill the plants. If the slope is all bellflower I would use a tank sprayer after cutting the plants off so as not to put a lot in the air spraying a tall plant.

If an area is more than 75% weed killing everything and renovating is the most practical in terms of reward for the amount of effort. But…. Bellflower is everywhere and unless your neighbors make an effort to control it, your bed isn’t a big contributor (by %) to the problem.

That must be so frustrating. All the rain is making weeds very robust this year as well as more desirable plants. Maybe next year won’t super charge weeds.

https://extension.umn.edu/weeds/creeping-bellflower
The information on the fact sheet doesn’t tell those of us who much but it does talk about how to eradicate it.