I raised beagles for yrs. All you have to do is take them where the rabbits are. If they have it in them (and most do) they'll run. Now whether they hunt /run like you want them to is where the dilemma begins.
Your basset, from what little experiance I've had with them . . .I've owned one and knew others with them . . .should make a good trail dog. I've seen them used for rabbits, deer, and what I may buy one soon for, to use to blood trail deer that have been wounded but did'nt go down. I'm color blind and it's hard for me to spot blood on the ground. Where I hunt mostley it's so thick you can walk right by a down deer and not see him. A basset would be good for this.
The down side of a basset in my opinion (at least with mine) is that they will follow their nose in a direction and for some reason seem not able or just plain don't care to find their way back.
Such was the case with mine and I finally lost him.