Use subdomain to mask URL on the top-level domain (specific page)

I was a little hesitant to ask since there is a wealth of knowledge on this topic, but am having a bit of trouble finding the specific case example here.

I have a form on one of my domains, and I want to setup a subdomain that will bring up that form w/o redirecting the url to the other domain.

form: mydomain.com/my-form sub-domain: enter-your-data.mydomain.com

I want the guest to go to (and end up at) enter-your-data.mydomain.com and fill out the form there. But the form is being run by mydomain.com

I don't have access to apache in this case so I've got limited (no) ability to setup a virtual host.

I do have access to rewrite rules which is how I think it can be done, but having issues where the url doesn't get rewritten.

I could do as an iframe but thats kind of a lousy way.

I could do something via php, but am looking for a "cleaner" way.

Thanks for your advise!