The phrase "deep bucket" means having a large amount of something, usually referring to resources, money, or talents. It suggests that one has a great capacity to handle or possess a significant quantity of those things. Full definition
Inside, the cabin has been stripped back to its bare essentials where deep bucket seats with a five - point race harness have been added. (autoexpress.co.uk)
To prevent the fleas from jumping out, be sure to use a fairly deep bucket and fill the bucket only halfway. (1800petmeds.com)
But the stripped out, driver oriented ethos and deep bucket seats are bound to figure. (carmagazine.co.uk)