Thule Racks does have a roof rack load bar adapter system called the Thule 532 Ride-On, allowing you to then connect a Thule fork mount bike carrier to the 532. Unfortunately, the 532 adapter is not compatible with your Hyundai Tucson load bars. That is why Thule Racks is recommending a whole new Thule load bar system. However a much cooler and cheaper way to go is the
Rocky Mounts Noose SL fork mount bike rack. The RockyMounts Noose SL will connect directly to your 2006 Hyundai Tucson factory bars and works great with both mountain bikes and road bikes. The Rocky Mountain Noose SL is well built, durable and easy to use and transfers from vehicle to vehicle as well. It's a fork mount bike rack, so you'll have to take the front wheel off first. But the bike will ride much more securely than an upright mount carrier that doesn't require taking the front wheel off. I also suggest getting a RockyMount key and lock core for each bike rack too, this will lock the bike to the rack.