Yours might be bugged then. I tested bandages myself to respond to another thread on bleeding.
I got like 16 or 18 stacks of bleed on me from the dancers at The Den, stepped off the side of the small cliff and used a bandage. After 5 seconds the bleeding was gone. Bleed normally lasts for 20 seconds.
But you can also use antidotes to cure it instantly. Or dodge.
Edit::
Found the post where I had tested bandages.
If bandages don’t work for you, I recommend recording a video of them not working and using that to create a bug report.