there is a way to shorten the url for gmail hosting services, all you have to do is to create a CNAME record in your DNS Server.
For example, this is the long URL to access to the gmail hosting service.
https://google.com/a/mydomain.com
Create a CNAME record in your DNS server.
mail IN CNAME ghs.google.com.
then when you type
http://mail.mydomain.com
it will redirect to your gmail hosting url
https://google.com/a/mydomain.com