Given that the relay contact bounce test circuit is still on the breadboard I recorded the time delay between 555 pin3 level change and relay NC/NO contacts state change. Using that very same circuit without any modification, I connected channel 1 probe to 555 pin3 and channel 2 probe to VO. Ground clips of both channels are connected to circuit ground. Channel 1 is set to 2V/div while channel 2 is at 5V/div--so that the two waveforms don't overlap one another on the screen. Trigger is set to single sweep, edge triggering on channel 1. Each screenshot below is a unique acquisition.
A. 555 pin 3 output rising, NO contacts closing. Time delay ~10.5ms (excluding contact bounce, i.e. delay is measured from 555 pin 3 rising edge to the very first falling edge of NO contacts)
B. 555 pin 3 output falling, NO contacts opening. Time delay ~8.6ms
C. 555 pin 3 output rising, NC contacts opening. Time delay ~7.3ms
D. 555 pin 3 output falling, NC contacts closing, Time delay ~12.2ms (excluding contact bounce)