Confused on how to setup BIND correctly

[Jason]

Hello everyone.

Well, I think im confusing myself more than anything else at this point. 
  Thought i'd call in for some reinforcements.

Here is what im attempting to do.

Our ISP currently hosts our DNS record for our domain. I would like that 
to continue for the time being. Now, in the meantime, I setup a BIND 9.2 
server that is only being used by our internal network to serve up 
private address that are only accessible by our LAN. Here is an example 
of how users access our private web servers (address wise)

webserver1.internal.mydomain.com

What I would like to do, if possible, is remove the 'internal' part of 
the name so they would only need to use:

webserver1.mydomain.com

Yet, this IP address would not be publicly available.
Also, if my users query mydomain.com, they answer would be pulled from 
our ISP's DNS server, not our private DNS server.

I may incorrect in this method, and if I am, please let me know. If 
there is a better way, I am all ears.

I know the easiest solution is for us to host our own DNS, which is 
where we will go eventually, but it's not possible at this point in time.

I appreciate the help. I look forward to your responses.

Jason