Normally strut failure makes it to where they are ineffective in dampening the movement of the vehicle on the springs.
This wouldn't cause a "rough" ride but in fact the opposite making it very soft and wavy. Where you'd hit a bump and the car would bounce multiple times as it settles back down on the springs. The strut reduces that movement allowing the suspension to move to absorb the initial impact without continuing to bounce.
The potential for the strut to cause a rough ride would be if it had seized instead of losing its pressure. If the shock seized to the point where it won't move at all or takes a lot of force to do so, then it would cause it to carry more of the road imperfections to you.
A bad bushing will allow the component to move more. This can have multiple effects depending on how the component fits. It may allow for a metal on metal contact, which can transfer a lot of vibration. On the other hand, it can move around more and not send as much through as it isn't held in place. A new OEM bushing or an aftermarket polyurethane can make you feel the bumps slightly more, but is an acceptable trade off for the improved handling and driver feedback. When you go to turn the vehicle, with bad bushings fractions of seconds are lost making the "turn in" of the car happen later as the components shift in place before they stiffen and then push the car instead of moving themselves.
If the feeling is there all the time and doesn't seem to be directly related to road conditions, there might be a wheel out of balance (circular balance, where the weight around the circumference of the wheel isn't even), a flat spot on a tire (can be caused from a hard braking event or sitting for an extended period of time not in use).
It may also need a front end alignment, especially if they didn't do one after taking apart the control arms for the bushings. If your toe or camber are far enough out, it could be causing a noticeable effect. If you don't hold onto the steering wheel on smooth pavement, does the car track straight or shift to the left or right? That is one sign of misalignment.
If you've used any of that spray fix-a-flat products, I've heard of people having bad vibrations after the use of those as you are spraying material inside of your tire with no way of getting it in there evenly.
Unfortunately many things can be the cause of a "rough" ride.