Hi,
Edwiser Bridge has various extensions and one of such plugin is the Single Sign-On plugin.
Single Sign-On provides end users with an option to enter a single username and password on the WordPress website and gain access to WordPress as well as Moodle simultaneously.
Which means the problem that you are facing will be sorted by using this plugin. When your users' login to WordPress and buy a course they will be redirected to the Moodle website and they will be already logged in and can access the course directly.
Hope this plugin solves your problems.