Even when cucumbers are bitter they're still very safe to eat.
Cucumbers become bitter because of an organic compound that occurs in the cucumbers when growing which is natural and still safe for consumption.
You can get rid of the bitter taste from cucumbers by cutting the end off and rubbing the cucumber which will remove that compound and make the cucumbers taste better.
I've eaten bitter cucumbers before and it's never made me sick but they just don't taste as good when they're bitter.