I don't have any experience with bougies so I have no idea as to how quickly they will root.
Are these Semi-hard wood or soft wood cuttings? You are using simply water?
https://evergreengardenworks.com/cuttings.htm : A bit about cuttings there.
A bit on Boagies here: https://www.bonsai4me.com/SpeciesGuide/Bouganvillea.html
B4me says wrt Propagation:
Softwood cuttings in early Spring, semi-ripe cuttings in Summer, air-layer in Autumn or Spring.
Wrong time of year [for one thing], Do you have any additional heating or lighting/humidity going on? Rooting hormone? They may just take a while under the best of circumstances and out of season may not be helping....
Roots do look like 'white clusters' for a while until they get their growth on. You may want to ride it out for a few more weeks and see what develops. How long have these been going?
Just a few ideas,