This is a difficult problem to deal with. I haven't heard of it in bassets, but I've seen it in other breeds. You need to try looking at ways to keep him quiet (perhaps crating) long enough for it to heal properly. Talk to the vet, although bandaging tails is very difficult. I've know dogs who had to have their tails amputated becuase they were continually splitting open the ends from banging them on things. I temporarily fostered a pit bull mix with this problem, he left blood on my walls going up and down the stairs.