Simple and straightforward

Note- you have to have a Bullseye account to use this. At the time of writing this, they have a free tier available but I believe you need a paid account to use the WordPress embed.
Just put in your Bullseye account details, and put the shortcode where you want it to show up. That’s about it.
I installed the plugin for a customer who had signed up for the Bullseye service. It was not working correctly, so I put in a support request and in a little over a week, an updated version was released, which worked just fine.
Note– if you prefer not to use the plugin, you can also do the integration yourself without too much sweat (which I did while waiting for the update), but the plugin does do some nice things (e.g. resizing the iframe so that the footer moves down when your search results come in). Overall, the result is pretty good for an iframe, and it even behaves acceptably on mobile.