What I said before was based in a recent Chambers Dictionary. Chambers 20th Century Dictionary of both 1964 and 1983 has just "a list or set of customs duties: a list of charges". Going back to Dyche's dictionary of 1777 gives "the rate or publick custom to be paid by those who import or export goods; also a table ready computed to shew the amount of various quantities of goods, etc.". That last bit is less clear (to us) - are those "amounts" money, charges, customs, or what? But the two fundamental meanings of customs duties, and a list of charges (not quite the same as prices) are consistent.
Exactly where the word got used most at any time is more a matter of idiom, or custom in the other sense, than meaning. It also crops up in news reports somewhat randomly, for example for channel tunnel fares, as well as the more common places such as hotels, electricity, and similar. I suspect it use for a bar and buffet tarif was customary in the 60s, and perhaps seem as a bit upmarket due to the association with hotels.
And was a price list compulsory in bars or anywhere else? It is now, but the earliest regulation I can find is the Price Marking (Drinks on Premises) Order 1975. To my surprise, there are questions in Parliament (both Hansards) that make it clear this was the first such order. Ransacking my poor old memory, I now think perhaps price lists were not always found in bars, and those there were tended to be placed where they were hard to see. So making them easy to find was good practice, adopted by businesses that wanted to make it clear they were not out to cheat anyone. And of course those (like BR) who were feared by potential customers to be expensive would need to reassure them just how much they were in for.