Man, I was just thinking about this the other day! I had a 'Paperwhite' narcissus bulb kit I bought on a whim last December, trying to bring some life into my gloomy apartment. From my experience, if you're starting with a pre-chilled bulb (which most of the ones you buy for indoor forcing are), it's a pretty quick process. I planted mine in a shallow pot with some pebbles and water, and I swear I saw the green tip poking up within like, four or five days. From planting to full bloom was maybe three weeks? Let's say 20 to 25 days on average.
The thing is, 'quick' is relative. You've got to keep them cool and bright once they sprout, or they get all leggy and flop over. I made that mistake my first year – stuck them on a warm windowsill and ended up with a sad, tangled mess of stems that needed staking. If you control the temperature a bit, keep them in a spot that's cool but sunny, the stems stay shorter and sturdier. The actual blooming period once the buds show color is super fast, maybe a couple of days from tight bud to fully open flower.
I've read that if you start with a bulb that hasn't been pre-chilled, you're looking at a much longer timeline, like 12 to 15 weeks because you have to simulate winter dormancy in your fridge first. But for the typical holiday 'just add water' kits, three weeks is a solid expectation. The wait feels longer when you're checking every morning, but seeing those pure white flowers finally open is totally worth it.