Short Wheel Base recumbents have quicker steering that regular diamond frame bicycles, the trick is keep you head up, focus some where down the road, look where you want to go, rather than where you are.. if you're constantly looking down, you're more likely to go down.
Hold on to the handlebar lightly, use the smallest effort to steer, speed could be your friend to keep the recumbent more stable. Check out the recumbent section on this forum, you may get more helpful tips.
Good luck.