TTM is technique sensitive, if you are off even a little on the day the fish needs to be moved then it will not work. If fish carries parasite or cyst during the final transfer then it will not work. With TTM you are using the lifecycle of cryptocaryon irritans and moving the fish as the parasite falls off to reproduce. Far from full proof. It can be done successfully, but can easily fail. My biggest gripe is you have to be 100% sure it is cryptocaryon irritans and not something else, and not a combination of parasites.
To answer your question, I’ve never tried to do TTM with buckets, but others have with success.
I have done TTM in combination with hypo with success, but it was more luck than anything. Way too much work for me to try again.
Either way, I wish you luck and hope the fish recover,