There is one turn when leaving work that has a small bump in the road. It is a long sharp curve and it always pisses me off because it bumps the car from my line and screws me up when entering the next turn. Do sways help cut down on bump steer?

 

On lowered rear-wheel drive cars, bump-steer is reduced by installing adjustable (longer) tie-rod ends in the front. I don't know if the same fix applies to lowered front-wheel drive cars though. If your car is stock height, I think Honda engineers already did the best they could to reduce bump-steer.

Aftermarket swaybars should help a bit since the stronger bar would eliminate a slight amount of independent wheel travel up and down which would mean less changes to the wheel's camber on bumps.

 

Typically the tighter/stiffer your suspension setup is, the more likely it is to be affected by road irregularities.

The sway bars reduce the amount of independence your front and rear wheels have because of the stiffer bar connecting them. For example, If I try to pull out of a slopped parking lot at an angle my inside front tire can come completely off the ground (maybe by an inch or two) so that when I punch the gas it spins like mad and when it finally touches the ground, it lets out a loud azz squeal which promptly draws the attention of anyone around. (Not good if the 5.0 is nearby)

If you are in the middle of a sweeping turn and hit a bump, the car will often "hop" sideways as a result of the suspension being tighter if you have aftermarket springs and shocks and what not.