Right now, your older female is asserting that this is
her house and
her family - especially with a young puppy, the alpha dog wants to set the ground rules up straight away, just like you will with your own rules (ie. chewing, peeing in the right places, barking, etc.). This means she needs to be a bit bossy and "distant" right now.
We adopted a 5 year old female German Shepherd, about 6 months ago, to join our 4 year old male German Shepherd. For about 2 weeks, our male growled when the female went near his toys or food bowl and followed her around constantly to make sure she wasn't breaking any of "his" rules. He also "supervised" her whenever she was interacting with "his" humans and would shoulder-check her out of the way when she was getting too friendly and he thought her visit time was up. We had a few dog fights during those two weeks, as well - they always lasted less than 3 seconds and both dogs backed down and walked away at the end of each. After two weeks, our male shepherd totally calmed down and stopped enforcing his rules - our female knew who the boss is, so there was no point in pushing it. Our female shepherd now cheerfully steals our male's toys and squeaks them in his face to get him to chase her, barks at him to distract him while he's trying to catch the frisbee, and they will spend an entire day stealing a single bone from each other while the other isn't looking, while the other bone lies untouched on the floor.

For his part, our male shepherd "snuggles" our female whenever he can and they recently shared a small kennel together while being boarded.
I wouldn't worry about it. The first few days are all about setting ground rules, but after that everyone seems to calm down. One thing to make sure of though, is that if your basset is going "too far" - you'll know what this is - harassing the puppy without end after the puppy "screws up", or starts getting overly physical in a "mean" way, you need to protect the puppy from the basset. Use your leg or arm to gently push her away from the puppy and sternly tell her "no" while holding her in place. This isn't so much to actually protect the puppy, but to reinforce in both their minds that no matter what silliness is going on between them, you are still boss and your rules are still at the top. It also reassures the puppy that he is in a safe place where the pack leader (you!) will keep him safe, even from other pack members.
Good luck! I'm sure your basset hound will be good-naturedly tolerating the puppy antics in no time!