Most Bassets have a condition called entropion. This involves usually the lower lids being curled outwards which exposes the membrane below the lids (the conjunctiva) to the air. In addition when the dog blinks the eyelids don’t sweep across the cornea (the eye surface) as efficiently as they should. The end result of this is that the eyes tend to be red most of the time and worse in dry, dusty or windy conditions.
Now is it “normal”? We tend to accept this as being a part of the breed characteristics. But it’s important to watch for signs of infection/inflammation because with entropion this is more likely. If the white area surrounding the eye (the sclera) is excessively red and in particular if he shows signs of discomfort (closing the lids, rubbing at the eyes) then you should have the eyes assessed by your vet. Note that entropion is not the only cause of reddening of the sclera.
In some cases of entropion surgery is recommended.
I hope I have been of help.