Host your plugin in a private repository on BitBucket and have Wordpress pick up every new release and update like normal.

Installing

Inside your plugin folder:

composer require maneuver/bitbucket-wp-updater

Usage

In your main plugin file:

require('vendor/autoload.php');

$repo = '';                 // name of your repository. This is either "<user>/<repo>" or "<team>/<repo>".
$bitbucket_username = '';   // your personal BitBucket username
$bitbucket_app_pass = '';   // the generated app password with read access

new \Maneuver\BitbucketWpUpdater\PluginUpdater(__FILE__, $repo, $bitbucket_username, $bitbucket_app_pass);

NOTE: Read more about BitBucket app passwords

Update the version number inside your main plugin file:

/*
Plugin Name: Awesome Plugin
Description: This is what your awesome plugin does.
Version: 1.0.0
Author: Your name
*/

And tag the commit:

git tag v1.0.0

NOTE: Use basic SemVer notation (a leading 'v' is allowed).

Caveats

Only works on activated plugins. For now.