I'm in the "only ever seen one a day on my island" camp. I don't TT and I regularly beach comb clearing out shells throughout the day (I have a shell bed in a corner of a beach where I dump them for when I want to craft shell furniture or get a "sell ten shells" nook miles task--don't clog up my inventory or count against the five star rating, win-win-win).
But I agree with
@Khaelis about the 10-20% chance of getting one on a mystery tour. That's the only time I've ever gotten a second bottle in a day. I have one character on my island.