CiviCRM (on WordPress) runs too slow to be useful
The problem isn't WordPress, but Hostmonster.  Shared hosting makes its money on sites that don't need any CPU or memory - simple WordPress sites, for instance.

CiviCRM is a much more resource-intensive program than your typical CMS (like WordPress).  If you have good shared hosting - which is hard to come by! - then you can sometimes run a very small CiviCRM instance.  Say, 500 contacts.

Consider a VPS instead.  Hostmonster offers a VPS service, but there are cheaper VPS vendors available.  If you're committed to shared hosting, there's a list of hosting providers available - but if you have the resources to support a VPS, you'll be much happier.