If the path isn't rewritten properly for the Manager, the odds are that it won't be for the front-end either.
I have sites in subdirectories at Bluehost and everything is accessible as mydomain.com, so that's definitely possible.
One quick check would be to put an index.html file in the MODX root with this content:
<h2>I'm in the MODX root</h2>
Then go to crssp.com/index.html in your browser and see if the message shows up. If not, Bluehost doesn't have the virtual domain set up properly -- nothing to do with MODX.
Assuming that that works, check this:
In the .htaccess site in the MODX root (where the manager and core directories are) should have a section that looks like this (assuming that you have Friendly URLs on):
#Options +FollowSymlinks
RewriteEngine On
RewriteBase /
# Rewrite www.domain.com -> domain.com -- used with SEO Strict URLs plugin
RewriteCond %{HTTP_HOST} .
RewriteCond %{HTTP_HOST} !^crssp\.com [NC]
RewriteRule (.*) http://crssp.com/$1 [R=301,L]
The directory *above* the MODX root directory (public_html) doesn't need an .htaccess file. If there's one there, it probably shouldn't have any rewrite rules.
One other thing to consider is the FURL settings. If FURLs are turned on in the modx_system_settings table, you need an .htaccess file with the rewrite rule above. If FURLs are off, you shouldn't have an .htaccess file in the MODX root.
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PLEASE, PLEASE specify the version of MODX you are using.
MODX info for everyone:
http://bobsguides.com/modx.html