The apostrophe was dropped from Bettys about fifty years ago, and the exact reason has become lost over time.
The general belief is that the name looked better without one, standing out as more distinctive – and, being a brand name, it wasn't governed by the usual linguistic rules. Numerous trademarks and brand names have eschewed conventional rules for similar reasons, a trend that has grown with the advent of internet domain names and email addresses.
Taylors has never had an apostrophe as the 's' is a plural to reflect the fact that various family members were involved in the company.