I have a Chev Cavalier, also 1995, doing the exact same problem. Bucking/hesitating at moderate throttle that goes away if I stomp on it. No stumble during idle.
I was thinking it has something to do with the EGR because if I plug up the vacuum going to the EGR the symptoms go away. Also if I disable any piece of the EGR system (for example the MAP or O2 sensor) symptoms go away. My theory is that something is giving the computer bad information and the computer is opening the EGR at the wrong time, imitating a giant vacuum leak. The car starts bucking as soon as I leave the driveway, but the EGR isn't supposed to open until you hit operating temperature.
I replaced plugs, wires, fuel filter, MAP sensor, EGR valve, TPS, IAM, coolant sensor,crankshaft sensor...just about everything in the EGR system. I can do this because I have a 96 Cavalier in the next stall and I can grab parts from it for free. Problem is I'm starting to suspect the PCM because in addition to something in the EGR system going haywire I also can not get a scan. Took it to both Autozone and Adavanced Auto and at both places the scanner said can't make a connection or can't link. Check out the PCM and visually it looks okay, meaning the wires weren't all coroded. Was hoping that I would find a bad wire or green ground. No such luck.
If you find out what's wrong with you car, post it because I may have the same problem.