Stairs are tough on Bassets and their spines. With their heavier front end, the going down compresses their discs according to out vet. Also it puts tons of stress on their front leg joints, which aren't great anyway due to the dwarfing of the breed, and the crooked joints.
We have stairs and our bedroom is upstairs. Bogie goes up at night to sleep by our bed and down in the morning. Otherwise we have a baby gate across the stairs and he is down stairs otherwise.
We got him at eight months, and carried him up and down, and waited unitl he was 10 months, and heavier, and started letting him learn the stair routine. Took about a month of keeping him on a leash and going very slowly for him to get proficient. The coming down is the tough part for them to get co-ordinated and Bogie's is kinda of a hopping motion with both front legs together and the two rear legs together. Pretty funny to watch, but works for him.
Our other Basset, Bubba, we lost to cancer in December developed disc problems at seven years. The vet said it was due to the jarring of the spine from stairs, and jumping up and down from couches and chairs. Bubba would make every trip we made up and down all day long. So Bogie has a ramp to get in SUV, stairs only one time a day, and no furniture.
Hope this helps. I'm sure others on the forum can answer better than I have.