I wonder whether "bucket" is an American shorthand term better avoided in this context. IME, BA call centre agents are perfectly able to understand the term "booking class", which is what I normally use; ba.com uses "selling class", which may also work just as well on the phone.

There are many industry standard terms which have a distinctly American flavour which are safe (and often better) to use than the British equivalents. For example, although the BA board has many instances of "single" and "return" tickets, the industry standard terms are "one-way" and "round-trip", and I try to use them in my posts. In particular, in this case, the term "a single ticket" is ambiguous, requiring context to distinguish between "a one-way ticket" or "only one ticket". But I think that "bucket" is more likely to be shorthand and therefore not within this category.