First off, the show needs to be clearly promoted. People need to know what they are being asked to attend. To people who don't listen to jazz, the word itself is ambiguous. When one person thinks of jazz, they may think of Sade or Spyro Gyra (smooth jazz) while another may think Coltrane or Davis (BeBop, Hard Bop). Even people who are hardcore jazz fans won't know what kind of entertainment you are planning. So, it's necessary to include samples of the band's music, a picture (the way the band looks can be a clue to their sound), and, at the very least, a shot list of artists they sound like. If they are all acoustic, say it. Any way you can let the potential audience know what to expect the better. Remember, it's not like rock or country in which the genre is mostly self describing. Be specific.
Secondly, if you are not a "jazz venue" DON'T OVER DO IT. If you had a band come in and your joint was packed, don't book them three more times that month. Let it rest. If you have another jazz band/artist to book then spread it out. If you only have one to book, don't bring them in more than once a month but every-other would be better.
**Artists, don't accept bookings at the same place that are too close together. You will suffer in the not-so-long run.**
Third and finally, PROMOTE it right. Don't run a radio ad for a jazz band on a classic rock radio station. That's just dumb. The people looking for live jazz are not going to be glued to that station. Your regulars will hear about it from being at your establishment or from talking to other regulars. Know your target. Facebook adds are cheap and very targetable. Flyers are cheap and still very effective (at the right places) and including a QR code linked to your website will make it even better.
Remember, people aren't going to come out and spend their hard earned money if they don't know about it. Don't rely on word of mouth. Smart advertising is the prerequisite for word of mouth and is the best way to create a buzz for something new. Make it easy to remember and easy to come to (dress codes not recommended). Jazz is people's music; It's life music. It's not dinner at the White House.