What I would do is first do a check on all the backlinks that their domain has.
If there is anything of value that would actually bring in some traffic, then it could be worth it. SEO-wise, Google has often said that when domains change hands and the content on them, the old links are devalued close to zero.
If you do buy it - do as you said, with a farewell notice, or try a 301 permanent redirect.
If you are doing the redirect, you might get some "mechanical" bookings by people who haven't even noticed that it is a different property. And you might guess how that will go when they arrive at the wrong address with the wrong assumptions.
If I were in your shoes, I would avoid all these complications.
But what I would definitely do is write a "Farewell dear colleagues" post on my blog, mentioning their name a couple of times, so that if their old customers will Google something like: "Is Gotham B&B closed?", they would get your website at the top..
