Does nitrate take a particular long time to percolate from surface into groundwater?
I know in New Zealand we have a number of soils you can't raise dairy herds on because the nitrate in their urine strips too many nutrients too fast, to the point where one can tell where the cow urinated a couple of weeks ago because that patch of grass is dying from several different deficiencies simultaneously. My understanding is that dairy cows are, hands-down, the worst farm animal for this because they stand still when voiding and dump up to 15 litres of moderate-high nitrate liquid waste at a time which all goes effective straight down through the soil column robbing it of nutrients along the way. On the other hand there are also some soils, generally in more arid areas, where nitrate doesn't migrate right through the soil column at all but concentrates in the subsoil as a visible, white, salty, horizon.

As a rule the more water retentive the soil the longer water soluble compounds like nitrate will take to work down into the ground at a given water input. There are also some chemical interactions that will bind nitrate and slow it down more than you might expect we need study them in my soil fertility papers but I can't think what they are right now.

But to answer your question, usually soluble soil ions (which nitrate is) move on a timescale of days, weeks or maybe months, but not decades. We wouldn't need to apply slow-release nitrate fertilisers annually if it didn't migrate through at least the top-soil relatively rapidly.