The actual length of the timeframe varies by Gnome (and potentially GM), but Bleaching is a multi-year process.
Every year that gnomes fail to find new and exciting experiences, the process accelerates: they become more depressed and withdrawn, and their dulled curiosity leads to them having less desire to seek out new experiences, which leads inexorably to further bleaching.
Additionally, based on Gnomes of Golarion p7 and 25, it seems like the rate of Bleaching is inversely proportional to age.
Mechanically, in Pathfinder 1e, Bleaching is "treated as a Curse" that cannot be removed with magic. Details are provided on p25 of GoG for GM's that wish to have mechanical rolls associated with the Curse. It forces an annual check starting at Middle Age.
Also on GoG p25, it is confirmed that a gnome given proper stimulus can halt or even reverse the process of Bleaching. There is even a society (GoG p12) called the Wonderseekers that commit themselves to identifying Bleaching gnomes and presenting them with opportunities to save themselves.
Additionally, it is possible to survive Bleaching through a stroke of luck (or other reasons). However, the alternative to reversing the Bleaching is becoming a Bleachling
Those rare few who manage to survive the affliction’s ravages and come
out the other side as the dreamy, pale beings known as bleachlings...
For more information, the sourcebook would be Gnomes of Golarion (GoG). Information here is from the Pathfinder Wiki portions that directly reference GoG.