How old is your basset? They were bred as tracking/hunting dogs, and when needed they can book it, even if their legs are pretty stubby. Instead of getting yet another dog that you have said yourself you don't have the time to invest in, take out your existing dog with you. Even if he/she is older, you can ask your vet about some good joint supplements. Especially in a breed that is easy to let get overweight/obese, the trails will do it some good.
I still agree with CP that herding breeds are your best bet...however, like photog said, if you go with that type of dog you'll need to search around and find a farm/ranch in your area that works cattle or sheep and also uses their dogs to breed. Make sure you see the mom AND dad in action, as well as how they interact with you, their owner, the other dogs, and the animals....just because they have it in their genes to work an animal doesn't mean they won't be aggressive/prey driven. Especially with Australian Cattle Dogs and blue heelers, if not properly exposed to smaller dogs they can get a little excited/nippy around them.
But, to be frank, just getting an animal that you can "play with" on the weekends is cruel. Dogs are not horses, they are actually the exact opposite...where as horses live to be lazy, dogs are predatory animals, they run, jump, play, bark, etc etc.
Sorry if this comes off as kind of preachy, I just hate to see perfectly good animals waste away inside...I'm trained in animal behavior and I work at a doggie day care, so dogs are like my life! lol, If you have any questions feel free to PM me.