If you have the room could you add on a strip of new planting area to the existing mounded bed. By that I mean butt a strip starting at the same grade of the existing bed but grade the new addition with a more gentle slope to correct the steep edge that is causing you your problem. If you're like me you'll be happy to have more planting area and it will be full in no time.
The width of this new corrective band will depend on how much room you can afford or want to add on. Depending on space you don't have to use a band you could add on an entire new bed etc.
Just an idea.
All the best & happy gardening.

I too had the same problem with the large nugget bark mulch, and found that using the shredded mulch underneath with the bark on top worked much better - the shredded mulch held things in place and did not wash out.

Hello there, Kanuk's options are a far better solution. I had used shredded mulch and also some heavier mulches before - to no avail. Any deluge of rain will simply wash away the mulch. (I didn't know shredded mulch could float) Your bed probably requires a correction in it's grading, possibly it's time to create mini-tiers to control the speed of how the water flowed out.

In my yard since the deluge was so strong, I ended up mulching with small stones and adding plants such as siberian irises and creepers to break up the flow.

Now you can go shopping for more plants & blame me!! lol
Let us know how it turns out.