For clarification stairs are not going to have an effect on hip dysplasia. While bassets are natorious for bad hips when talking hip displasia as a dissease process and not simply joint lacticity and ppor joint fit very few bassets actual have a problem. breed with substaintial better hips like GSD's and Labs have much more problems as they age. This is because bassets carry less weight on the rear most of their weight is carried by the front end, have larger joint surfaces to disperse the forces better (largerest bone mass of any breed) and short limb length but less force on the joints than their longer legged brothern. The biggest single thing you can do to aleived hip problems as the dog ages is to maintain proper weight. It is clearly shown that over nutrition play as important if not more important role in hip dysplasia than genetics.(I carry her down the stairs because I read about hip dysplasia)
The reason to limit stairs is two fold. 1 it is thought the extra force of going down the stairs can adversly effect the dogs back. To be honest there is scant evidence to suport this theory. 2. Is that bassets tend to be clumsy as puppies and a fall trip when decending staire can lead to a traumatic and permanent injury considering the softnes and fraility of a puppies bones. 3. is that basset already have less than ideal groth plates. This is the area of the bones that all growth occurs. they are dwarf and changes to the groth plates are responsible for the deminished growth in length of the long bones of the leg, Their growth plates may be more frail and eassily damaged than other breeds. Damage to the growth plate will cause the bone to stop growing. this can cause severe othoropeadic annomally's like angular limb deformaties. than can only be repaired surgically. If damage occurs when the dog is older the bones have less time to continue to grow so the effect is less. hence the Limitation of stair recommended any where between 6 month and a year.