I read that Nelsons had bought the Bach Centre. Is this true?

No.

A judgement issued at the end of the 1990s, after a legal action brought by Healing Herbs Ltd. against Nelsons Ltd., included the erroneous claim that Bach Centre Mount Vernon Ltd. had been sold to Nelsons in 1993. This is not true.

Certainly, a company of a similar name was sold to Nelsons in 1993, as part of the sale of the Centre’s remedy production business. But Bach Centre Mount Vernon Ltd. was not sold, and like the rest of the Bach Centre continues to be run as part of an independent organisation. See also the question, Who owns the Bach Centre?