Yes you ceratinaly can. We offer WordPress through our Installatron script library which is included for Free with every Bluebird web hosting package. This allows you to install a Wordpress site in minutes without any prior experience.
If you already have a WordPress site, your current Hosting company should allow to to back it up, install WordPress on our servers, and then restore your site.
If you need any assistance in moving your WordPress site to Bluebird or for installing WordPress please contact us in the support department and it will be a pleasure to help you.