Is there a way to disable the user from being able to change the "Owner" field in CB Invites?
No, normal users can't see or use it. It's for moderator usage only. Unless all your users are moderators there shouldn't be any cause for concern, but if all your users are moderators then the owner field is least of your issues.
would also like to know if there was any way to control the form that is used?
It's completely template based and can be edited from the below location.
components/com_comprofiler/plugin/user/plug_cbinvites/templates/