Basically you have to use a Bootstrap class and declare it on elgg-plugin.php.

As a sample you can check the latest release of this plugin https://elgg.org/plugins/1937889.

Also have a look on the plugins of Coldtrick team at https://github.com/coldtrick. Their latest releases are developed without the start.php file.

Thank you both for your suggestions. I will look at the examples you provided and try to learn more about how to use a Bootstrap class and declare it in the elgg-plugin.php file. While I am pretty good at HTML, CSS and writing documentation, I am still learning PHP. 

For others interested in learning more about how to move code from start.php to elgg-plugin.php using the bootstrap class, there are a couple of Elgg tutorials that might help:

http://learn.elgg.org/en/stable/guides/plugins.html

see also this guide

http://learn.elgg.org/en/stable/guides/plugins/bootstrap.html