This is a subject near to my heart.....I've never owned bassets, but have kept and raised beagles over 20 years. I've had a few hundred hounds.......several hundred weren't worth feeding.........had probably 40 good ones, 3 great ones, and one really great one (This one finished 2nd in the UBGF Nationals)..........
There are several magazines that feature rabbit hounds........Hounds and Hunting, The Rabbit hunter, and Better Beagling just to name a few.......there are still AKC Field events for bassets.......Hounds and hunting used to publish the field trial results, but I haven't seen bassets listed for the last several years.....there are a few left that make rabbit hounds, but most have went the way of the Irish Setter and Cocker Spanial..........First thing is genetic......hounds either have it, or they don't..........it's 80% blood, and 20% or less training........you can't change the way a hound runs, or the way he barks...you can't make them run........you can correct, to a point, what he runs, and minor flaws with improper use of voice.......among other things...but only to a point....
You don't mention the age or sex of your dog, and the very best time to start a hound on game is when they are shedding their puppy teeth, or around 5 months........older dogs will usually start, but don't seem to start as easily as a pup..........the breeding behind a hound has a lot to do with how easily a hound starts, and several studs, when bread to known bitch lines are known to produce pups that start easily........other studs and blood lines, when bread to the same bitch line are known to be harder to start......this usually has nothing to do with the quality of the hound once started however........They usually start easier when the weather is moist, and the air temp is with in 9 degrees of the ground temp.......this is what makes a really great hound, he can do a good job running in any scenting conditions by adjusting his speed to compensate for the conditions.......ideally, he should run with no checks (momentary loss of scent).....but to do this slows the hound to the point where they are not useful to hunt with.......so, they should work off the point of loss, but not have many break downs......and the great ones have a method they use every time to regain the scent, or "line." Great hounds have gears.....they go slow when conditions are tough.....and air it out when the scent is high.........to fast and they crash...or loose the line and the rabbit.....not a good thing.......accountability for the rabbit is a must....the great ones loose very few.....and can run the same rabbit for hours without a loss provided the rabbit will run and not go to a hole.......if your hound is loosing rabbits, you have a real problem.......
What is popular, is to take the hound to a "starting pen". This is a small enclosure with lots of rabbits. Enclosures are used to show the hound as many rabbits as necessary until the hound smells, and harks........I like to get mine out of the enclosure as soon as the hound opens on game, as such a small space leads to problems if left in to long..........this is the fastest way to get one started.............You can do the same thing in the wild, but this takes longer unless you've got a spot with a lot of rabbits.......
If you have a friend that already has a running dog, you can also cast your hound with his..........I won't do this, unless I know the quality of the hound I'm putting mine down with........hounds learn bad habits fast.......
I've seen one fellow who would trap a live rabbit.....and put the rabbit in a very small enclosure.........maybe 50 feet by 50 feet.......put the hound on a 45 foot rope and stand in the middle of the enclosure.........the rabbit will run the edges of the pen, or risk being eaten...........If you have any genetics at all, the dog should start sight chasing the rabbit becoming more and more excited..........when your convinced the dog is ready, catch the dog, then the rabbit........hold the dog and let the rabbit loose followed closely by the dog......hopefully, the hound will run it a little way before loosing it.........
There are other things to try, such as dragging a dead rabbit on a string then following a minute or so later with the dog........I'm not much on this way.......
The main reason people have hounds that aren't great is that it takes time and effort to find out what a good one is, what the desirable traits of a trailing hound are, and what the flaws are..........I think you can down load an AKC rule book which is mostly rules and procedures on how to run a field trial, but has a section on desirable and undesirable qualities.........One thing I've learned over the years.......it cost the same to feed a good one as it does to feed a bad one............you usually have to go through a few to get a good one, so try not to get to attached........treat them like pro football players........being a Cowboy fan, Dorsett was great, but when his time was up and he couldn't produce Jerry Jones traded him to Denver.........It's hard to do, but the successful houndsmen cull ruthlessly.....
Hope I answered part of your question anyway........