You could probably plant low-growing or trailing plants that bees like around the edge of your raised courgette bed. Linaria, Nasturtium, lamb's ear are some examples. Tall plants (for example, zinnia, coneflower) would probably lead to the competition problem you mentioned.
If you are mainly wanting to attract pollinators, try letting nearby kale, broccoli or something similar go to flower, if you have them. Any good candidate flower that actually is in the raised bed should not be competing with the courgettes for sunlight and space (and having the flower eventually shaded out should not be a problem for you).
Finally, you can grow your flowers in larger pots that are outside of the bed, but nearby, and which can be moved around if needed.
