Hello Boylesg, scope probes can give overshoot or under shoot but rarely real ringing (several cycles), on breadboard - the extra capacitance on this medium is notorious for extra effects such as ringing, which changes completely when you go to a pcb, no doubt you have a bit of flying lead wiring inductance + capacitance from the bread board that gives the ringing on the edges, certainly put 470nF and 4u7 right across the 555 which will help a little, I assume you are using the modern Cmos version of the 555? To compensate for your wiring L & C (on the bread board) to reduce the ringing you can add a snubber at the receiving end of the signal path, start with 1nF and 220 ohm (in series, placed from o/p to gnd) this should take out the worst of the ringing - you can experiment with values, on a good pcb layout with good de-coupling (caps across the 555 power) you may not need any snubbing - see how you go... good luck..!